Three-Dimensional Quantum Black Holes: A Primer

In the paper

“Indeed, one must account for both the black hole and cosmic string, leading to a modified first law including variations of the tension of the cosmic string [118][119][120][121].”

What the sources say

• Disputed

  The paper accounts for the black hole and cosmic string, but it explicitly holds the string tension fixed. In the passage surrounding Eq. (16) (labeled Abstract in our copy), it requires δμ = 0 and derives a first law without a tension-variation term. The concluding discussion likewise says the string cannot change tension. (LLM, conf=0.89)

  Checked by a reasoning model — may be wrong.

  cites [118] Appels, 2016, Thermodynamics of Accelerating Black Holes, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Supported

  The Introduction (§1) says the paper derives a first law for black holes with varying conical-defect tension. Section 2 gives the modified first law with a term for variation of cosmic-string tension, accounting for the black hole–string system. (LLM, conf=0.94)

  cites [119] Appels, 2017, Black Hole Thermodynamics with Conical Defects, J. High Energy Phys. source
• Supported

  The Abstract identifies the conical singularity attached to the black hole as a cosmic string whose tension drives acceleration. In the FIG. 1 section, Eq. (11) gives a first law with variations of both string tensions, and the text following Eq. (12) explicitly says the authors allow those tensions to vary. (LLM, conf=0.94)

  cites [120] Appels, 2018, Holographic Thermodynamics of Accelerating Black Holes, Phys. Rev. D source
• Not checked yetcites [121] Appels, M. (2018). Thermodynamics of Accelerating Black Holes. [PhD Thesis, Department of Mathematical, Durham University].

In the paper

“Since the bulk geometry is simply vacuum AdS, it evades the no-go theorem of[66].”

What the sources say

• Disputed

  The paper states that its no-go result requires no assumptions about the bulk spacetime; it identifies M = 0, not vacuum AdS bulk geometry, as the case that escapes. Our copy labels this passage “Abstract” and provides no page number. (LLM, conf=0.91)

  Checked by a reasoning model — may be wrong.

  cites [66] Bruni, 2001, Gravitational collapse on the brane, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“More specifically, in a large-N expansion, the planar diagram limit of the CFT, the bulk is well-approximated by classical gravity (we will state this dictionary more precisely below).”

What the sources say

• Partly supported

  The D3-brane discussion (p. 5) identifies quantum effects in the bulk with 1/N effects in the gauge theory and suggests that the large-N master field is an anti-de Sitter supergravity solution. But it also says supergravity calculations can be trusted in a coupling regime where gauge-theory calculations cannot; the planar large-N limit alone is not presented as sufficient for a classical-gravity approximation. (LLM, conf=0.83)

  cites [6] Maldacena, 1998, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. sourceExperimental — accuracy not yet measured

In the paper

“Crucially, the geometry of the end-of-the-world (ETW) brane is dynamical, having an induced theory of gravity.”

What the sources say

• Supported

  Section 1, “Warped Compactifications and AdS/CFT holography” (page not supplied), says the bulk spacetime ends on the brane and that gravity becomes dynamical there. Section 2 derives Einstein’s equation for the induced brane metric, supporting the claim that the brane has an induced theory of gravity. (LLM, conf=0.94)

  cites [11] Skenderis, 2001, Gravity in warped compactifications and the holographic stress tensor, Class. Quant. Grav. source

In the paper

“Meanwhile, classical black holes do exist in three-dimensional Einstein gravity with a negative cosmological constant [30,31], a consequence of the tendency for gravitational collapse afforded by the negatively curved geometry.”

What the sources say

• Supported

  On p. 1, the authors state that a black-hole solution exists in 2+1-dimensional Einstein theory with a negative cosmological constant. They explicitly say they first ignore the Maxwell field, so the result supports the claim about Einstein gravity. (LLM, conf=0.95)

  cites [30] Banados, 1992, The Black hole in three-dimensional space-time, Phys. Rev. Lett. source
• Supported

  The Abstract describes black holes in standard Einstein theory in 2+1 dimensions with a negative cosmological constant. Section 2.5 identifies the horizon of a solution that describes a black hole. These passages support the existence claim attributed to the source. (LLM, conf=0.94)

  cites [31] Banados, 1993, Geometry of the (2+1) black hole, Phys. Rev. D source

In the paper

“The precise form of the brane action likewise follows from a modification of holographic renormalization [19,73,74], where the counterterm action exactly truncates (see also [75,76]).”

What the sources say

• Partly supported

  The Conclusions (section 6; page unavailable) say that counterterms can be reinterpreted as an action for bulk modes localized on a brane. Appendix B says the divergent counterterms form a finite, dimension-dependent set, but it does not say that a modified holographic-renormalization procedure yields the precise brane action or that the counterterm action exactly truncates. (LLM, conf=0.84)

  cites [19] Solodukhin, 2001, Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence, Commun. Math. Phys. sourceExperimental — accuracy not yet measured
• Partly supported

  Section 2, “The regularization procedure” (page unavailable), describes cancelling divergences with covariant counterterms to obtain a finite effective action. It does not derive the precise form of a brane action or say that a modified counterterm action exactly truncates; its finite list of divergent terms is not that claim. (LLM, conf=0.84)

  cites [73] Henningson, 1998, The Holographic Weyl anomaly, J. High Energy Phys. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The discussion around equations (12)–(14) derives a Liouville boundary action in 2+1-dimensional gravity and notes when an additional counterterm is unnecessary. The later discussion mentions holographic renormalization, but neither passage addresses a brane action or says that a counterterm action exactly truncates (searched for both). Our copy provides no basis to verify the attributed claim. (LLM, conf=0.74)

  cites [74] Carlip, 2005, Dynamics of asymptotic diffeomorphisms in (2+1)-dimensional gravity, Class. Quant. Grav. sourceExperimental — accuracy not yet measured

In the paper

“The rotating and charged holographic quantum black holes, meanwhile, do not match to the non-holographic perturbatively-corrected counterparts (cf.[27,40,45]).”

What the sources say

• Partly supported

  In “Comparison to perturbative backreaction” (page unavailable), the paper finds that the rotating holographic and perturbative solutions have different radial dependence and substantially different quantum corrections. That supports the rotating part of the claim, but the paper does not make a corresponding comparison for charged quantum black holes. (LLM, conf=0.88)

  cites [27] Panella, 2023, Quantum Kerr-de Sitter black holes in three dimensions, J. High Energy Phys. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [40] Steif, 1994, The Quantum stress tensor in the three-dimensional black hole, Phys. Rev. D source
• ?Could not verify

  The Rotating Black Hole section reports perturbative quantum corrections to rotating black holes, but does not compare them with holographic rotating or charged solutions. The Static Naked Singularity section discusses a holographic braneworld metric and says its horizon formation agrees with the authors’ results; that static comparison does not settle the claimed mismatch for rotating and charged black holes. Searches for holographic, charged, and comparative terms found no passage making that claim. (LLM, conf=0.76)

  cites [45] Casals, 2019, Quantum-corrected rotating black holes and naked singularities in (2+1) dimensions, Phys. Rev. D sourceExperimental — accuracy not yet measured

In the paper

“Such dilaton models of gravity admit exactly solvable black hole solutions including semi-classical backreaction, e.g., [85][86][87][88].”

What the sources say

• Supported

  The Introduction says the authors modify a two-dimensional dilaton-gravity model to make its semiclassical equations exactly solvable; it also identifies Hawking-radiation backreaction as part of the model. Section 2, “Exact solutions,” states that the resulting equations can be solved exactly and gives black-hole solutions. The claim is supported for this modified model, not for every dilaton-gravity model. (LLM, conf=0.92)

  cites [85] Russo, 1992, The Endpoint of Hawking radiation, Phys. Rev. D source
• Supported

  Section 2.3 (p. 13) says that adding a term for leading-order quantum backreaction to two-dimensional dilaton gravity led to semi-classical equations that can be solved exactly, specifically in the modified RST model. Section 2.4 (p. 16) describes the resulting semi-classical black hole solutions. The paper distinguishes this from the original CGHS equations, which it says have not been solved in closed form. (LLM, conf=0.92)

  cites [86] Susskind, 1993, The Stretched horizon and black hole complementarity, Phys. Rev. D source
• Supported

  Section II (pp. 10–12) describes a two-dimensional dilaton black hole model with semiclassical backreaction and states that the RST version can be solved exactly when a local counterterm is added. The paper therefore supports the cited example, with exact solvability applying to that modified model in the large-N approximation. (LLM, conf=0.91)

  cites [87] Fiola, 1994, Black hole thermodynamics and information loss in two-dimensions, Phys. Rev. D source
• ?Could not verify

  The Introduction and Detailed calculations discuss higher-dimensional black holes on a brane and their Hawking evaporation. Searches for dilaton gravity, exact solvability, and semiclassical backreaction found no passage addressing whether dilaton models admit the claimed solutions. (LLM, conf=0.76)

  cites [88] Emparan, 2000, Black holes radiate mainly on the brane, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“Combined, this leads to an effective dimensionless coupling g eff quantifying the size of the effects the CFT 3 has on the brane geometry [92]”

• Also stated in: § Karch-Randall braneworld holography · plain

  “g eff ∼ |I CFT | |I Bgrav | ∼ G 3 c 3 L 3 . (4.22)”

What the sources say

• ?Could not verify

  Section VI discusses higher-derivative corrections to five-dimensional black holes and central charges of dual four-dimensional CFTs, not the effect of a three-dimensional CFT on brane geometry. Searches for the effective coupling, the action ratio, and three-dimensional brane backreaction found no passage establishing g_eff ∼ G3 c3/L3. Page numbers were unavailable in our copy. (LLM, conf=0.76)

  cites [92] Cremonini, 2010, Higher Derivative Corrections to R-charged Black Holes: Boundary Counterterms and the Mass-Charge Relation, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“For ℓ ̸ = 0, the non-vanishing components of the renormalized quantum-stress tensor (4.31) are found to be [25]”

What the sources say

• Partly supported

  The source lists five non-vanishing stress-tensor components in equations (3.20)–(3.24), each with an ℓ prefactor. But it explicitly says these are only the leading-order piece, T⁽⁰⁾; section 2.4, equation (2.43), includes higher-order terms. It therefore does not establish that the cited expressions give the full renormalized tensor for ℓ ≠ 0. (LLM, conf=0.84)

  cites [25] Emparan, 2020, Quantum BTZ black hole, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“When r -→ 0, i.e., κ c and κ + simplify to the surface gravities of the cosmological horizon and black hole horizon of the qSdS black hole [26].”

What the sources say

• Partly supported

  Equation (5.19) gives the surface gravities κc and κh for the cosmological and black-hole horizons of the qSdS solution. The paper does not state that κc and κ+ reduce to those values when r− → 0, so the claimed limiting relationship is unsupported by our copy. (LLM, conf=0.83)

  cites [26] Emparan, 2022, Black holes in dS3, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“the Nariai mass was found to live in the finite range [26] 11 27 < 8G 3 M < 1 ,(4.113)”

What the sources say

• Supported

  Equation (4.36) in our copy states the claimed range for the Nariai mass exactly. The surrounding discussion identifies the lower bound with the limit R₃ ≈ ℓ and the upper bound with R₃/ℓ → ∞. (LLM, conf=0.95)

  cites [26] Emparan, 2022, Black holes in dS3, J. High Energy Phys. source

In the paper

“In the near-horizon regime, the geometries appear as fibered products of a circle and two-dimensional anti-de Sitter, de Sitter, and Minkowski space, respectively.”

What the sources say

• Supported

  Section 3.3 describes the near-horizon extremal geometry as a fibered product of AdS₂ and a circle, the rotating Nariai geometry as dS₂ fibered over a circle, and the ultracold geometry as a fibered product of two-dimensional Minkowski space and a circle. These are the three geometries and the order stated in the claim. (LLM, conf=0.94)

  cites [27] Panella, 2023, Quantum Kerr-de Sitter black holes in three dimensions, J. High Energy Phys. source

In the paper

“In principle, the Penrose process of energy extraction in the qKdS solution in morally the same way as a classical four-dimensional Kerr-de Sitter black hole (see, e.g., [109]).”

What the sources say

• ?Could not verify

  Section 3.2 discusses conserved charges and black-hole thermodynamics, while section 6 relates warped dS₃ to a near-horizon limit of four-dimensional Kerr–de Sitter. Neither passage addresses Penrose-process energy extraction or compares how that process works in the two geometries. Searches for “Penrose process,” “energy extraction,” and “ergoregion” found no passage establishing the claim. (LLM, conf=0.77)

  cites [109] Anninos, 2011, Holography For a De Sitter-Esque Geometry, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“A first glimpse of this comes from Euler's theorem of homogeneous functions implies black holes with a non-zero cosmological constant Λ d+1 obey obey [141] (d -2)G d+1 M = (d -1)T S -2P d+1 V + ... ,(5.88)”

What the sources say

• Partly supported

  Section 2 derives the Smarr relation from Euler’s theorem for a static AdS black hole. Sections 3.2 and 5 supply the temperature, entropy, pressure, and volume identifications that give (d−2)M = (d−1)TS − 2PV when D = d+1. The cited paper does not place an additional G on the left-hand side under its stated conventions. (LLM, conf=0.83)

  cites [141] Kastor, 2009, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. sourceExperimental — accuracy not yet measured

In the paper

“Carefully taking the limit rN ≈ rh,c , the temperature Th,c of both horizons approaches the Nariai temperature T N = 1/(2πr N ) (see, e.g., Appendix B of [134]).”

What the sources say

• Partly supported

  Appendix B (eqs. B.13 and B.18) says that, with the Bousso–Hawking normalization, both horizon temperatures approach the Nariai temperature. But it gives T_N = 1/(2π L̄_d), not generally 1/(2πr_N); the stated formula holds in four dimensions, where r_N = L̄_4. (LLM, conf=0.88)

  cites [134] Svesko, 2022, Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“Thus, Hawking radiation from the brane perspective corresponds to bulk gravitational bremsstrahlung [22].”

What the sources say

• Supported

  Section 5 explicitly states that the bulk dual of Hawking radiation is gravitational bremsstrahlung. The paper presents this as a qualitative interpretation, not a fully worked-out bulk calculation. (LLM, conf=0.94)

  cites [22] Emparan, 2002, Quantum black holes as holograms in AdS brane worlds, J. High Energy Phys. source

In the paper

“The stability structure remains the same with branes included [202].”

What the sources say

• Supported

  In the black-string stability discussion (page not supplied), the authors say they checked that the earlier stability conclusion obtained without branes remains correct with branes present. They specify the scope: the string is stable for large horizon radius relative to the AdS length and unstable for small radius. (LLM, conf=0.91)

  cites [202] Gregory, 2008, Classical and quantum gravity of brane black holes, J. High Energy Phys. source

In the paper

“This is consistent with the Schwarzschild black string with a Randall-Sundrum brane construction in [69].”

What the sources say

• Supported

  Section 2.1 constructs a uniformly warped black string using a four-dimensional Schwarzschild metric and places a vacuum brane in the Randall–Sundrum setup. The cited paper therefore describes the construction identified by the citation; the citing authors’ statement that their result is consistent with it is their own comparison. (LLM, conf=0.92)

  cites [69] Fitzpatrick, 2006, On the existence and dynamics of braneworld black holes, J. High Energy Phys. source

In the paper

“In fact, whilst searching for examples of Oppenheimer-Synder gravitational collapse of braneworld black holes, a no-go theorem was posed [66]: the exterior geometry of the dust cloud cannot be static.”

What the sources say

• Supported

  The paper states that, under standard matching conditions on the brane, the exterior of a collapsing dust cloud cannot be static (passage 1, section labeled Abstract). Its abstract likewise describes a no-go theorem for Oppenheimer–Snyder-like collapse on a Randall–Sundrum-type brane (passage 7). (LLM, conf=0.94)

  cites [66] Bruni, 2001, Gravitational collapse on the brane, Phys. Rev. Lett. source

In the paper

“This theorem, and the dearth of evidence of exact static black holes localizing in the RS-II construction (circa 2002), in part motivated Tanaka [34] and Emparan, Fabbri, and Kaloper [22] to conjecture higher-dimensional braneworld black holes must be time-dependent (see also [198]).”

What the sources say

• Partly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [34] Tanaka, 2003, Classical black hole evaporation in Randall–Sundrum infinite brane world, Prog. Theor. Phys. Suppl. sourceExperimental — accuracy not yet measured
• Partly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [22] Emparan, 2002, Quantum black holes as holograms in AdS brane worlds, J. High Energy Phys. sourceExperimental — accuracy not yet measured
• Partly supported

  Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [198] Emparan, 2003, Black hole astrophysics in AdS brane worlds, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“Likewise, in the case of quantum BTZ, a computation of the heat capacity [176] reveals reentrant phase transitions occur in the canonical ensemble between thermal AdS and a branch of thermally stable quantum black holes.”

What the sources say

• ?Could not verify

  The Introduction and §2 identify the quantum BTZ black hole, but the paper studies weak cosmic censorship and mentions thermodynamics only as a topic of other work. Searches for heat capacity, the canonical ensemble, and reentrant phase transitions found no passage addressing the claimed transition between thermal AdS and stable quantum black holes. Page numbers were not available in our copy. (LLM, conf=0.76)

  cites [176] Frassino, 2024, Weak cosmic censorship and the rotating quantum BTZ black hole, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“When the bulk theory includes higher curvature and semi-classical quantum corrections, the RT formula (7.3) generalizes to the following extremization prescription [246]”

What the sources say

• Supported

  Section 3 proposes extremizing generalized entropy to obtain a quantum extremal surface for holographic entanglement entropy. Section 3.1 says that when the gravitational action is not Einstein–Hilbert, a corrected entropy functional replaces area in the extremization, and that higher-curvature and entanglement corrections must be treated consistently. The prescription is presented as a proposal, not a proven formula; no page numbers are available in our copy. (LLM, conf=0.89)

  cites [246] Engelhardt, 2015, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, J. High Energy Phys. source

In the paper

“By applying this doubly-holographic reasoning to higher-dimensional topological black holes [65], black strings [264,265], and de Sitter space [83,266], the prescription (7.6) yields unitary Page curves, except in cases where the horizon is extremal with a vanishing temperature.”

What the sources say

• Supported

  Split into 2 atoms — 2 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [65] Chen, 2020, Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane, J. High Energy Phys. source
• Partly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [264] Geng, 2022, Entanglement phase structure of a holographic BCFT in a black hole background, J. High Energy Phys. sourceExperimental — accuracy not yet measured
• Partly supported

  Split into 2 atoms — 1 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.

  cites [265] Karch, 2023, Subregion entropy for the doubly-holographic global black string, J. High Energy Phys. sourceExperimental — accuracy not yet measured
• Partly supported

  Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.

  cites [83] Neuenfeld, 2024, Liouville gravity at the end of the world: Deformed defects in AdS/BCFT, J. High Energy Phys. sourceExperimental — accuracy not yet measured
• Partly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [266] Geng, 2021, Information paradox and its resolution in de Sitter holography, Phys. Rev. D sourceExperimental — accuracy not yet measured

In the paper

“Indeed, while some bulk black holes get stuck on the brane and never shrink ('black droplets') [71] and hence dynamically stable, there are other bulk black solutions that evaporate due to a Gregory-Laflamme instability [72], as originally suggested in [22,34].”

What the sources say

• Supported

  Section 4.1, “Twin black hole evaporation,” describes a Gregory–Laflamme instability that makes the horizons on the branes shrink until none remain. This supports the claim attributed to this paper; the separate statement about who originally suggested the mechanism is assigned to other citations. (LLM, conf=0.91)

  cites [72] Emparan, 2023, Holographic duals of evaporating black holes, J. High Energy Phys. source
• Partly supported

  Section 5 (page unavailable) proposes that an evaporating brane black hole emits classical gravitational waves into the bulk and may eventually slide off the brane. It does not attribute that evaporation to a Gregory–Laflamme instability or establish that bulk black solutions evaporate by that mechanism. (LLM, conf=0.86)

  cites [22] Emparan, 2002, Quantum black holes as holograms in AdS brane worlds, J. High Energy Phys. sourceExperimental — accuracy not yet measured
• Partly supported

  Section VII (Summary and Discussion; page unavailable) proposes, explicitly as speculation, that black-hole evaporation in the five-dimensional picture could involve blobs escaping into the extra dimension; it relates their size to a black-string instability. Section VI (Black Hole and AdS/CFT Correspondence; page unavailable) also describes a black-string configuration as unstable. The paper thus supports an early suggestion of an instability-related evaporation mechanism, but does not establish that bulk black-hole solutions evaporate because of a Gregory–Laflamme instability. (LLM, conf=0.84)

  cites [34] Tanaka, 2003, Classical black hole evaporation in Randall–Sundrum infinite brane world, Prog. Theor. Phys. Suppl. sourceExperimental — accuracy not yet measured

In the paper

“According to [72,215], their semi-classical dynamics are always dual to classical Gregory-Laflamme-like dynamics of bulk black holes.”

What the sources say

• Supported

  The Outlook (section 6; page not provided) says that the physics of holographic CFTs coupled to black holes is “always dual to Gregory-Laflamme-type dynamics of bulk horizons.” The paper also describes holography as classicalizing Hawking evaporation (section 4.5), supporting the claim’s semiclassical-to-classical framing. (LLM, conf=0.91)

  cites [72] Emparan, 2023, Holographic duals of evaporating black holes, J. High Energy Phys. source
• Partly supported

  The Introduction and Summary says holography maps the evolution of Hawking radiation from two boundary black holes to classical gravity in AdS, and describes a Gregory–Laflamme-like instability of the connecting bulk black string when it is sufficiently thin. It does not establish that semi-classical dynamics are *always* dual to such an instability; its claim concerns this particular setup and condition. (LLM, conf=0.88)

  cites [215] Emparan, 2022, Black tsunamis and naked singularities in AdS, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“Thus far, there is agreement that the expectation value of the quantum stress tensor of a free scalar field diverges at the inner horizon of a RN or Kerr black hole (in D = d + 1 = 4) on approach from the exterior [296][297][298][299], suggesting a type of strong cosmic censorship.”

What the sources say

• Partly supported

  The Near-IH asymptotic behavior section reports that the trace of the renormalized stress-energy tensor diverges as the inner horizon is approached from within a four-dimensional Reissner–Nordström black hole. It does not establish divergence of the full stress tensor, and it explicitly identifies extension to Kerr as future work. (LLM, conf=0.90)

  cites [296] Lanir, 2019, Analysis of quantum effects inside spherical charged black holes, Phys. Rev. D sourceExperimental — accuracy not yet measured
• Partly supported

  In “Developing the near-IH flux expressions” (page unavailable), the paper finds that a component of the renormalized stress tensor diverges at the Reissner–Nordström Cauchy horizon when expressed in a regular Kruskal-like coordinate, as the horizon is approached from within the black hole. It also says the corresponding Eddington-coordinate fluxes approach finite values. The paper does not establish the stated divergence for a Kerr black hole, so the broader RN-or-Kerr claim is only partly supported. (LLM, conf=0.86)

  cites [297] Zilberman, 2020, Quantum fluxes at the inner horizon of a spherical charged black hole, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Partly supported

  Section 6 (Discussion; page unavailable) reports a study finding that the quantum stress-tensor trace of a massless scalar diverges at the Cauchy horizon of a specific four-dimensional, non-extremal Reissner–Nordström black hole. It does not report the corresponding quantum result for Kerr, and it does not specify an approach from the exterior for the Reissner–Nordström result. The paper’s own quantum calculation concerns BTZ black holes. (LLM, conf=0.87)

  cites [298] Dias, 2019, The BTZ black hole violates strong cosmic censorship, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“Originally achieved for models of two-dimensional dilaton gravity, 59 holographic braneworlds confirm unitary Page curves arise in higher-dimensional gravity [65,260].”

What the sources say

• Supported

  Section 4.2, “The Page curve in d > 2” (page not supplied), presents Page curves for braneworld black holes in dimensions d = 3, 4 and 5. It describes entropy rising before an island phase takes over at the analogue of the Page time, supporting the claim that higher-dimensional holographic braneworlds produce Page-curve behavior. (LLM, conf=0.90)

  cites [65] Chen, 2020, Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane, J. High Energy Phys. source
• Partly supported

  Section 2 describes a two-dimensional gravity model with a three-dimensional holographic dual and Planck brane. Section 3.3 finds that the radiation entropy rises and then falls—the Page curve—in that setup. The paper's Abstract says the authors argue for this result; it does not establish unitary Page curves for higher-dimensional gravity generally, as the claim's wording suggests. (LLM, conf=0.84)

  cites [260] Almheiri, 2020, The Page curve of Hawking radiation from semiclassical geometry, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“Consequently, as argued in [300], and verified in [301] using the techniques of [299], rotating quantum BTZ has a singular inner horizon.”

What the sources say

• Partly supported

  The Abstract argues that the inner horizon will become singular after next-order backreaction, supporting the attribution that this paper argued for a singular horizon. But §3.2 says the quantum-corrected BTZ solution is smooth at the inner horizon at leading order, so the unqualified statement that it has a singular inner horizon omits a decisive condition. (LLM, conf=0.86)

  cites [300] Emparan, 2020, Strong cosmic censorship in the BTZ black hole, J. High Energy Phys. sourceExperimental — accuracy not yet measured
• Supported

  Section 3.2 (“3D analysis”) explicitly says that quantum effects lead to a singular inner horizon in the rotating BTZ black hole. The paper distinguishes this from the smooth inner horizon possible in classical rotating BTZ. (LLM, conf=0.95)

  cites [301] Kolanowski, 2023, Singularities in 2D and 3D quantum black holes, J. High Energy Phys. source
• Supported

  The citation to this paper, [299], is attached to the techniques used for the verification, not to the singular-inner-horizon finding itself. Section 6 says the authors analyze BTZ using the methods of their previous section, supporting that methodological attribution. (LLM, conf=0.90)

  cites [299] Hollands, 2020, Quantum instability of the Cauchy horizon in Reissner–Nordström–deSitter spacetime, Class. Quant. Grav. source

In the paper

“Notably, the classical Penrose inequality can be violated at leading order in perturbative backreaction [311,312].”

What the sources say

• Supported

  Section II considers a perturbative quantum state and computes its contribution to the mass. It finds that negative quantum-field energy reduces the mass at infinity and violates the classical Penrose inequality; the violation is not merely higher-order in the semiclassical expansion. (LLM, conf=0.93)

  cites [311] Bousso, 2019, Quantum Penrose Inequality, Phys. Rev. Lett. source
• Supported

  Section 3, “Violation by Quantum Effects” (page unavailable), gives a counterexample: a Boulware-like quantum state reduces the mass by a parametrically small amount while leaving the trapped surface sufficiently unchanged, violating the classically saturated Penrose inequality. The appendix (“Additional information,” page unavailable) explicitly treats quantum matter as a small perturbation and expands the Einstein equation to first order in G. (LLM, conf=0.90)

  cites [312] Bousso, 2019, Quantum Information Bound on the Energy, Phys. Rev. D source

In the paper

“although the extra bulk spatial dimension becomes infinite in extent, the higher-dimensional gravity becomes localized on the brane nonetheless.”

What the sources say

• Supported

  The Introduction says the single positive-tension brane permits dimensional reduction without compactifying the extra dimensions. Section II says this model yields conventional gravity on the brane, supporting the claim that gravity is localized despite the noncompact extra dimension. Our copy provides no page numbers for these passages. (LLM, conf=0.88)

  cites [323] Sasaki, 2000, Gravity, stability and energy conservation on the Randall-Sundrum brane world, Phys. Rev. D source
• ?Not checked — no full text of the sourcecites [324] Garriga, 2000, Gravity in the brane world, Phys. Rev. Lett. source
• Supported

  The Introduction describes gravity localized near a brane in the Randall–Sundrum setup and says that a realistic model can have uncompactified extra dimensions. Section 3.2 explains that localization in such a space requires a normalizable graviton ground state; the claim describes this possibility, not an unconditional result for every infinite extra dimension. No page numbers are available in our copy. (LLM, conf=0.92)

  cites [325] Csaki, 2000, Universal aspects of gravity localized on thick branes, Nucl. Phys. B source

In the paper

“So far, Kerr-Newman black holes do not [302,303].”

What the sources say

• ?Not checked — no full text of the sourcecites [302] Wald, 1974, Gedanken experiments to destroy a black hole, Ann. Phys. source
• Supported

  The Introduction states that the authors’ analysis rules out violations of the Kerr–Newman black-hole condition through overcharging or overspinning. For slightly non-extremal black holes, the result assumes linear stability and accounts for second-order effects; the citing sentence’s “so far” does not claim an exception-free proof beyond that analysis. (LLM, conf=0.91)

  cites [303] Sorce, 2017, Gedanken experiments to destroy a black hole. II. Kerr-Newman black holes cannot be overcharged or overspun, Phys. Rev. D source

In the paper

“For holographic AdS black holes, quasi-normal modes appear as poles in relevant retarded two-point correlators of the dual CFT, providing a field-theoretic characterization of black holes out of thermal equilibrium [316].”

What the sources say

• Partly supported

  Section 2 (p. 5) says quasinormal modes are poles of a retarded Green’s function used to describe the bulk field’s decay. The Introduction (p. 2) and Conclusions (p. 21) connect that decay to perturbations of a thermal state in the dual CFT. Our copy does not identify those poles as poles of the CFT’s retarded two-point correlators, and its thermalization result concerns particular scalar perturbations of large AdS black holes rather than black holes out of equilibrium generally. (LLM, conf=0.86)

  cites [316] Horowitz, 2000, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D sourceExperimental — accuracy not yet measured

In the paper

“Loosely speaking, assuming there are no naked singularities and collapsing matter settles to a Kerr black hole, then the total mass M for a D ≥ 4-dimensional asymptotically flat [305][306][307][308] or AdS spacetime [309,310] with a marginally trapped surface σ is bounded below by the area A[σ]”

What the sources say

• Partly supported

  The Main Theorem proves a mass–area bound for asymptotically flat 3-dimensional spatial slices with minimal-surface boundaries. The Conjecture section proposes a related bound for an outermost surface in an asymptotically flat spacetime, but does not establish it for general marginally trapped surfaces or D > 4. The sentence cites other sources for AdS, so that part is not attributed to this paper. (LLM, conf=0.88)

  cites [305] Huisken, 2001, The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality, J. Differ. Geom. sourceExperimental — accuracy not yet measured
• Partly supported

  Section 13, Theorem 19 proves a mass–area lower bound for an outer-minimizing horizon in an asymptotically flat Riemannian 3-manifold. That supports the asymptotically flat part of the citation, but does not establish the stated bound for all D ≥ 4 spacetimes with marginally trapped surfaces. The sentence attaches separate citations to the AdS case, so that case is not assessed against Bray. (LLM, conf=0.88)

  cites [306] Bray, 2001, Proof of the Riemannian Penrose Inequality Using the Positive Mass Theorem, J. Differ. Geom. sourceExperimental — accuracy not yet measured
• Partly supported

  The Introduction and Theorem 1.3 state a mass lower bound in terms of horizon area for asymptotically flat manifolds. But the paper proves the time-symmetric Riemannian case for spatial dimensions less than eight, with an outer-minimizing minimal horizon; it does not establish the claim for all D ≥ 4 spacetimes with marginally trapped surfaces. The AdS portion has separate citations in the citing sentence and is not attributed to this source. (LLM, conf=0.88)

  cites [307] Bray, 2009, On the Riemannian Penrose inequality in dimensions less than 8, Duke Math. J. sourceExperimental — accuracy not yet measured

In the paper

“This implies, given the connection between hydrodynamics and chaos in holographic CFTs [318,319], the chaotic dynamics of black holes are dramatically altered when backreaction is accounted for.”

What the sources say

• Supported

  The citation is attached to the connection between hydrodynamics and chaos in holographic CFTs, not to the citing authors’ conclusion about backreaction. In the source’s Discussion (section labeled MIT-CTP; page unavailable), the authors state that black-hole scrambling and the holographic butterfly effect can be understood through a hydrodynamic sound mode. (LLM, conf=0.93)

  cites [318] Grozdanov, 2018, Black hole scrambling from hydrodynamics, Phys. Rev. Lett. source
• Supported

  The citation is attached to the connection between hydrodynamics and chaos, not to the citing authors’ subsequent inference about backreaction. The paper’s Discussion says its results support a connection between many-body chaos and energy conservation, and describes a hydrodynamic dispersion relation constrained by chaos parameters. (LLM, conf=0.92)

  cites [319] Blake, 2018, Many-body chaos and energy dynamics in holography, J. High Energy Phys. source

In the paper

“The h tt metic component is simply a modified Newtonian potential for a source M where the 1/r 3 correction can be shown to be precisely of the form of the corrections to the Newtonian due to 1-loop quantum effects induced by the four-dimensional graviton propagator [62,63].”

What the sources say

• Supported

  The discussion on p. 4 derives a 1/r³ quantum correction to the Newtonian potential for a point source. The abstract (p. 1) identifies one-loop corrections to the graviton propagator as its origin, and the discussion on pp. 6–7 reports agreement with the brane-world correction. (LLM, conf=0.93)

  cites [62] Duff, 2000, Complementarity of the Maldacena and Randall-Sundrum pictures, Phys. Rev. Lett. source
• ?Not checked — no full text of the sourcecites [63] Duff, 1974, Quantum corrections to the schwarzschild solution, Phys. Rev. D source

In the paper

“Considering probe fields of brane localized matter, dual to CFT operators with conformal dimension ∆ ∈ [1,2] and spin s = 0, ±1/2, it was found that the QNMs and their overtones exhibit qualitatively different behavior depending on the branch of the qBTZ solution selected.”

What the sources say

• Partly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [317] Cartwright, C., Gürsoy, U., Pedraza, J.F., and Planella Planas, G. (2024). Perturbing a quantum black hole. arXiv. sourceExperimental — accuracy not yet measured

In the paper

“In other words, the supergravity solution has a dual description in terms of the four-dimensional superconformal field theory, a sharp realization of the AdS/CFT correspondence [6].”

What the sources say

• Partly supported

  The D3-brane section (p. 5) links the AdS₅ × S⁵ supergravity solution to four-dimensional N = 4 Yang–Mills theory and calls the correspondence a new form of duality. But it says the solution is *suggested* to be the Yang–Mills master field and calls the correspondence a conjecture; the citing sentence presents the dual description as established. (LLM, conf=0.78)

  cites [6] Maldacena, 1998, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. sourceExperimental — accuracy not yet measured

In the paper

“Setting n = q = 0 in the metric functions (D.10) recovers the form of the C-metric used in [23,24] (cf.Eq. ( 5.1) of [24]).”

What the sources say

• Supported

  Section 3.1, Eqs. (3.1)–(3.2), gives the metric and its function G(x), and identifies the solution as a special case of the AdS C-metric. This supports the citation as identifying the C-metric form used in the source; the comparison with the citing paper’s Eq. (D.10) is the citing authors’ own calculation. (LLM, conf=0.90)

  cites [23] Emparan, 2000, Exact description of black holes on branes, J. High Energy Phys. source
• Supported

  Section 5 (“Adding rotation”) presents Eq. (5.1) as a rotating, accelerating black-hole metric and explicitly says it is neutral and has its NUT parameter set to zero. This supports the attribution of the zero-charge, zero-NUT C-metric form to this paper; (D.10) is the citing paper’s equation, not one the source needs to contain. (LLM, conf=0.90)

  cites [24] Emparan, 2000, Exact description of black holes on branes. 2. Comparison with BTZ black holes and black strings, J. High Energy Phys. source

In the paper

“The effect is that the non-factorized rotating C-metric will possess closed timelike curves in a neighborhood of the torsion singularities [341].”

What the sources say

• Partly supported

  The passage labeled “Closed timelike curves in general relativity > Abstract” says that CTCs exist in the vacuum spinning C-metric. It does not identify a non-factorized form or locate those CTCs near torsion singularities; its discussion of torsion singularities concerns a region between spinning particles. (LLM, conf=0.88)

  cites [341] Bonnor, 2003, Closed timelike curves in general relativity, Int. J. Mod. Phys. D sourceExperimental — accuracy not yet measured

In the paper

“Concerns that double-holography leads to superluminal signalling[60] are ameliorated when the brane description is treated as an effective theory, such that ETW brane models are consistent with causality[61].”

What the sources say

• Supported

  The citation to this paper is attached to the concern about superluminal signalling, not the subsequent claim about ameliorating it, which has a separate citation. Section 5 reports superluminal propagation in the intermediate picture, specifically for signals crossing between the brane and the non-gravitational region; it does not say signals travel faster than light within either region. (LLM, conf=0.92)

  cites [60] Omiya, 2022, Causal structures and nonlocality in double holography, J. High Energy Phys. source
• Partly supported

  The Abstract says that treating the brane description as an effective theory makes faster-than-light causality violations invisible above the cutoff length scale. It says this *suggests* that end-of-the-world brane models are consistent with causality; the citing sentence presents that conclusion without the source's qualification. (LLM, conf=0.82)

  cites [61] Neuenfeld, 2023, On the causality paradox and the Karch-Randall braneworld as an EFT, J. High Energy Phys. sourceExperimental — accuracy not yet measured

In the paper

“Perturbative corrections to black hole solutions in semi-classical new massive gravity give rise to logarithmic terms in the blackening factor[94].”

What the sources say

• ?Could not verify

  The Generalized Smarr Formula section discusses classical Kerr–Newman–AdS black-hole thermodynamics and identifies AdS corrections to the Smarr formula, not corrections to a blackening factor. Searches for semi-classical new massive gravity and logarithmic terms in the metric found no passage in our copy addressing the cited claim. (LLM, conf=0.76)

  cites [94] Caldarelli, 2000, Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories, Class. Quant. Grav. sourceExperimental — accuracy not yet measured

In the paper

“For example, the bulk and brane horizon temperatures coincide.”

In the paper

“One notable difference between the black hole (1.5) and the perturbative geometry (1.3) is that ℓ ∼ cL P ≫ L P , where c is the central charge of the cutoff CFT 3 on the brane.”

In the paper

“Further, the geometry (1.5) is an exact solution to the semi-classical brane theory.”

In the paper

“As we will see below, at least for the neutral, static geometries, the exact quantum black holes receive the same modifications to their geometry as suggested by the (non-holographic) perturbative analysis summarized in Section 2.”

In the paper

“Specifically, in the case of the static quantum BTZ black hole, large enough backreaction trigger reentrant phase transitions, e.g., a transition from thermal AdS to the quantum black hole back to thermal AdS.”

In the paper

“Nonetheless, the CFT is in a thermal state.”

In the paper

“Further, with the conical singularities removed, the final bulk solution no longer has a cosmic string.”

In the paper

“In particular, the geometry (4.26) is an exact solution to the gravitational field equations of the semi-classical induced action (4.19)”

In the paper

“This brings the C-metric line element (4.1) to the form”

• Also stated in: § 4.1 Bulk geometry: AdS C-metric · plain

  “which is recognized to be empty AdS 4 , foliated by AdS 3 slices with radius L 4 cosh(σ) at constant σ.”

What the sources say

• Not checked yetcites [25] Emparan, 2020, Quantum BTZ black hole, J. High Energy Phys. source

In the paper

“The upper bound follows from studying for the end behavior of M (x 1 ), with x 1 = √ 3 (excluding x 1 = -√ 3 on account of the parameter range (4.8)) at κ = -1 being a maximum.”

In the paper

“Recall the bulk geometry will retain conical singularities at the remaining roots of G(x) (not x = x 1 ).”

In the paper

“Further, the Green function obeys analyticity properties shared by the Hartle-Hawking state, a state describing a black hole in thermal equilibrium with its own radiation.”

In the paper

“To see this, first note the central charge c 3 of the CFT 3 is normalized such that”

• Also stated in: § Karch-Randall braneworld holography · plain

  “c 3 = L 2 4 G 4 = ℓ 2G 3 √ 1 + ν 2 ,(4.20)”

• Also stated in: § Karch-Randall braneworld holography · plain

  “where we introduced the parameter ν ≡ ℓ/ℓ 3 .”

In the paper

“Keeping m, L 4 , and ρ finite, the limit ℓ → ∞ results in”

• Also stated in: § 4.1 Bulk geometry: AdS C-metric · plain

  “the metric for static, neutral AdS 4 black holes (further clarified upon transforming x = cos θ).”

In the paper

“In either case, notice the leading order contribution to the stress-tensor is not of the standard thermal type, i.e., diag{-2, 1, 1}.”

In the paper

“For κ = -1, the boundary geometry (ℓ → 0) has a black hole with horizon radius r + = ℓ 3 .”

In the paper

“In this set-up it is possible to write down a host of analytic braneworld black hole solutions to the bulk field equations plus Israel junction conditions.”

In the paper

“Note, moreover, relative to ζi , the surface gravity, defined via ζi ∇ i ζj = κ + ζj , is”

• Also stated in: § 4.2.1 Static quantum BTZ · plain

  “κ + = η 2 |H ′ (r + )| = 1 2 |H ′ (r + )| = 1 2ℓ 2 3 2r + + µℓη 3 r2 + ,(4.36)”

In the paper

“Thus, the qBTZ solution has negative and positive masses.”

In the paper

“Lastly, 25 Evidence of the G3 identification in (4.27) is that the relation can be derived exactly by integrating the bulk volume in the action with a bulk IR cutoff as r → ∞ [23].”

• Also stated in: § 4.2.1 Static quantum BTZ · plain

  “the form function F (M ) (4.28) is purely a function of mass M because it depends on M only through x 1 and is otherwise independent of ν = ℓ/ℓ 3 .”

What the sources say

• Not checked yetcites [23] Emparan, 2000, Exact description of black holes on branes, J. High Energy Phys. source

In the paper

“In this case, upon substituting (4.11), a brane at x = 0 has tension τ = 1 2πG 4 ℓ .”

In the paper

“To rid ourselves of the acceleration horizon, it is sufficient to work in the case where ℓ > L 4 .”

In the paper

“The limiting geometry (4.6) also shows black holes appear for µ ̸ = 0.”

In the paper

“This suggests the positive mass solutions subdivide along the range x 1 ∈ (0, √ 3) and x 1 ∈ ( √ 3, ∞), smoothly joining at x 1 = √ 3.”

In the paper

“To complete the space, a second copy of the 0 ≤ x ≤ x 1 region is glued along x = 0, resulting in a Z 2 -symmetric double-sided Karch-Randall braneworld.”

In the paper

“Then, treating the x = 0 hypersurface as a cutoff brane, excising the x < 0 region leads to a spacetime free of conical singularities.”

In the paper

“Fixing the period of ϕ in this way, the spacetime will have conical singularities at the remaining roots of G(x).”

In the paper

“Further, since it is the combination κx 2 1 that appears in all physical quantities of interest, the negative mass branch and the positive mass branch with x 1 ∈ (0, √ 3) smoothly connect at x 1 = 0.”

In the paper

“The conical singularity at x = x 1 , for example, is removed via the identification”

• Also stated in: § Horizons and bulk regularity · plain

  “ϕ ∼ ϕ + ∆ϕ , ∆ϕ = 4π |G ′ (x 1 )| = 4πx 1 3 -κx 2 1 .”

In the paper

“Treat the root x 1 as a primary parameter while µ is derived from x 1 via”

• Also stated in: § Horizons and bulk regularity · plain

  “µ = 1 -κx 2 1 x 3 1 .”

In the paper

“Notice higher-curvature corrections enter at quadratic order.”

In the paper

“Nonetheless, the static black hole attached to the brane is in an accelerated frame.”

In the paper

“Indeed, the Green's function from which ⟨T ij ⟩ is derived (in the perturbative treatment) is periodic in imaginary time with a period given by the (inverse) Tolman temperature [42].”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [42] Lifschytz, 1994, Scalar field quantization on the (2+1)-dimensional black hole background, Phys. Rev. D source

In the paper

“Further, from (4.21), we see for fixed c 3 then gravity becomes weak (G 3 → 0) as ℓ → 0.”

In the paper

“In the limit ℓ → 0, this corresponds to the surface gravity of the classical BTZ black hole.”

In the paper

“Aside from the match of the perturbed geometry, the leading order contribution to ⟨T ij ⟩ (4.33) agrees with the renormalized stress-tensor of the free conformal scalar (except L P → ℓ).”

In the paper

“Further, it is worth emphasizing that the solution (4.26) consistently solves the semi-classical brane equations of motion for any ℓ > 0, including large backreaction effects (ν > 1).”

In the paper

“Alternatively, as the tension becomes larger, ℓ → 0, it follows σ b → ∞, i.e., the brane is pushed to the asymptotic boundary of AdS 4 .”

In the paper

“In the limit of vanishing rotation, κ + becomes the surface gravity of the static qBTZ, (4.36).”

In the paper

“Demanding there are no naked singularities requires µ to be bounded below by µ (κ) ext , i.e., the value of µ when the bulk black hole becomes extremal.”

In the paper

“Further, varying with respect to the gauge field A i , we find the analog of the semi-classical Maxwell equations,”

In the paper

“Due to the ∼ µ/r 3 behavior in each of the remaining components, up to unimportant factors, the large-r structure of (4.64) essentially depends on F (M, J) as defined in (4.66).”

In the paper

“In particular, the 'naive metric' (4.42) unexpectedly no longer has a ring singularity, but instead a curvature singularity at r = 0.”

In the paper

“When the bulk theory of gravity is Einstein-Maxwell, the induced brane action (4.15) receives corrections due to the bulk Maxwell contribution, such that the induced brane action is now”

In the paper

“The coordinates (t, r, ϕ), however, are not canonically normalized due to the periodicity in ϕ (4.44).”

In the paper

“Hence, the leading order stress-tensor only depends on backreaction effects via G 3 and not G 3 M or G 3 J.”

In the paper

“Using H(r ± ) = 0 and assuming r + ̸ = r -, it is straightforward to express”

In the paper

“Removal of a conical singularity at, say x = x 1 (denoting the smallest positive root of G(x)) has us simultaneously perform a coordinate transformation t = t+ax 2 i ϕ together with the periodicity condition for ϕ”

In the paper

“For example, substituting normalized coordinate (4.51) into ⟨T tt ⟩ 0 , yields”

In the paper

“At x 1 = √ 2 one attains an extremal bound, where M = J/ℓ 3 = 1/4G 3 .”

In the paper

“For the quantum black hole, however, for any value of J, this classical extremality bound is violated, M ≤ J/ℓ 3 , when -κx 2 1 < 2ã 2 , giving rise to 'super-extremal' black holes among the branch 1 solutions.”

In the paper

“In canonically normalized coordinates ( t, r, φ), the inner and outer horizons of the quantum black hole are generated by orbits of the canonically normalized generator (4.56), i.e.,”

In the paper

“As an exact solution to the semi-classical theory (4.81), the geometry (4.85) is recognized as the 'charged' version of the quantum BTZ black hole.”

In the paper

“There is an analogous set of branches for non-vanishing J, where, in particular, branches 1b and 2 meet at a maximum value of M for fixed J.”

In the paper

“Upon imposing bulk regularity conditions (equivalent to those for the neutral, static geometry), the induced geometry on the brane at x = 0, in terms of canonically normalized coordinates (t, r, ϕ) = (η t, η -1 r, η φ), is [99] (see also [100])”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [99] Feng, Y., Ma, H., Mann, R.B., Xue, Y., and Zhang, M. (2024). Quantum Charged Black Holes. arXiv. source
• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [100] Martinez, 2000, Charged rotating black hole in three space-time dimensions, Phys. Rev. D source

In the paper

“Explicitly, for arbitrary κ, the extremal mass is [99]”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [99] Feng, Y., Ma, H., Mann, R.B., Xue, Y., and Zhang, M. (2024). Quantum Charged Black Holes. arXiv. source

In the paper

“Moreover, the periodicity alters the asymptotic form of the metric such that the dtdϕ would instead grow as r 2 , implying a diverging angular momentum.”

In the paper

“Still, the quantum black hole (4.85) is charged.”

In the paper

“Further, the surface gravities vanish in the extremal limit, i.e., where the inner and outer black hole horizons coincide, r + = r -.”

In the paper

“The r 2 -divergence can be ameliorated by changing coordinates (t, ϕ) to ( t, φ) where,”

In the paper

“Taking r i to be real, ζ 2 = 0 when H(r i ) = 0, where r i are positive real roots of H(r) (4.41) (restricting to a coordinate range where there exists at least one real root).”

In the paper

“Notice the mass (4.54) and angular momentum (4.55)only depend on ã and κx 2 1 and not on ℓ.”

In the paper

“The metric equations of motion of the induced theory to order O(ℓ 2 ) are as the neutral case, except now with an additional contribution coming from the F 2 contribution in the action.That is,”

In the paper

“In particular, the electric charge is”

In the paper

“Further, unlike the static solution (4.33), the stress-tensor for the rotating qBTZ black hole is not characterized by a single function F (M ).”

In the paper

“Geometrically, the qBTZ line element (4.26) takes the form of global AdS 3 .”