CoChat
Sign Up
Cited by 125

The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.

Quantum instability of the Cauchy horizon in Reissner–Nordström–deSitter spacetime

Hollands, Stefan, Wald, Robert M, Zahn, Jochen·2020·Classical and Quantum Gravity
DOI 10.1088/1361-6382/ab8052
Open this paper in CoChat — free account

Abstract

In classical general relativity, the values of fields on spacetime are uniquely determined by their values at an initial time within the domain of dependence of this initial data surface. However, it may occur that the spacetime under consideration extends beyond this domain of dependence, and fields, therefore, are not entirely determined by their initial data. This occurs, for example, in the well-known (maximally) extended Reissner–Nordström or Reissner–Nordström–deSitter (RNdS) spacetimes. The boundary of the region determined by the initial data is called the ‘Cauchy horizon.’ It is located inside the black hole in these spacetimes. The strong cosmic censorship conjecture asserts that the Cauchy horizon does not, in fact, exist in practice because the slightest perturbation (of the metric itself or the matter fields) will become singular there in a sufficiently catastrophic way that solutions cannot be extended beyond the Cauchy horizon. Thus, if strong cosmic censorship holds, the Cauchy horizon will be converted into a ‘final singularity,’ and determinism will hold. Recently, however, it has been found that, classically this is not the case in RNdS spacetimes in a certain range of mass, charge, and cosmological constant. In this paper, we consider a quantum scalar field in RNdS spacetime and show that quantum theory comes to the rescue of strong cosmic censorship. We find that for any state that is nonsingular (i.e., Hadamard) within the domain of dependence, the expected stress-tensor blows up with affine parameter, V , along a radial null geodesic transverse to the Cauchy horizon as T VV ∼ C / V 2 with C independent of the state and C ≠ 0 generically in RNdS spacetimes. This divergence is stronger than in the classical theory and should be sufficient to convert the Cauchy horizon into a singularity through which the spacetime cannot be extended as a (weak) solution of the semiclassical Einstein equation. This behavior is expected to be quite general, although it is possible to have C = 0 in certain special cases, such as the BTZ black hole.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1088/1361-6382/ab8052

Cites

3 of 3 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The classical rotating BTZ black hole is a notable exception where backreaction is mild enough that the inner horizon does not become singular, indicating a violation in strong cosmic censorship.

    “A notable exception, however, is the classical rotating BTZ black hole, where the backreaction is mild enough such that the inner horizon does not become singular, indicating a violation in strong cosmic censorship [298,299].”

    From Three-Dimensional Quantum Black Holes: A Primer (2024) · cites this paper as [299]

  • Rotating quantum BTZ has a singular inner horizon.

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

    From Three-Dimensional Quantum Black Holes: A Primer (2024) · cites this paper as [299]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Flagged first, then by citations

Research works printed but not linked: 68

  1. Hintz, 2017, Analysis of linear waves near the Cauchy horizon of cosmological black holes, J. Math. Phys., 58, 10.1063/1.4996575 · DOI
  2. Dafermos, 2018, Rough initial data and the strength of the blue-shift instability on cosmological black holes with Λ > 0 {x=[ ]}, Class. Quantum Grav., 35, 10.1088/1361-6382/aadbcf · DOI
  3. Boulware, 1973, Naked Singularities, Thin Shells, and the Reissner-Nordström Metric, Phys. Rev. D, 8, 2363, 10.1103/physrevd.8.2363 · DOI
  4. Poisson, 1990, Internal structure of black holes, Phys. Rev. D, 41, 1796, 10.1103/physrevd.41.1796 · DOI · Paper page
  5. Mellor, 1990, Stability of Black Holes in De Sitter Space, Phys. Rev. D, 41, 403, 10.1103/physrevd.41.403 · DOI
  6. Mellor, 1992, A reassessment of the stability of the Cauchy horizon in de Sitter Space, Class. Quantum Grav., 9, L43, 10.1088/0264-9381/9/4/001 · DOI
  7. Brady, 1998, Cosmic censorship: As strong as ever, Phys. Rev. Lett., 80, 3432, 10.1103/physrevlett.80.3432 · DOI
  8. Dias, 2018, Strong cosmic censorship: taking the rough with the smooth, J. High Energy Phys., 10.1007/jhep10(2018)001 · DOI
  9. McNamara, 1978, Behaviour of scalar perturbations of a reissner-nordström black hole inside the event horizon, Proc. R. Soc. A, 364, 121, 10.1098/rspa.1978.0191 · DOI
  10. Dafermos, 2003, Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations, Ann. Math., 875, 10.4007/annals.2003.158.875 · DOI
  11. Dafermos, 2005, The Interior of charged black holes and the problem of uniqueness in general relativity, Commun. Pure Appl. Math., 58, 0445, 10.1002/cpa.20071 · DOI
  12. Dafermos, 2014, Black holes without spacelike singularities, Commun. Math. Phys., 332, 729, 10.1007/s00220-014-2063-4 · DOI
  13. Luk, 2017, Proof of linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations, Duke Math. J., 166, 437, 10.1215/00127094-3715189 · DOI
  14. Costa, 2015, On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant: I. Well posedness and breakdown criterion, Class. Quantum Grav., 32, 10.1088/0264-9381/32/1/015017 · DOI
  15. Costa, 2015, On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: Structure of the solutions and stability of the Cauchy horizon, Commun. Math. Phys., 339, 903, 10.1007/s00220-015-2433-6 · DOI
  16. Franzen, 2016, Boundedness of Massless Scalar Waves on Reissner-Nordström Interior Backgrounds, Commun. Math. Phys., 343, 601, 10.1007/s00220-015-2440-7 · DOI
  17. Costa, 2017, Bounded energy waves on the black hole interior of Reissner-Nordström-de Sitter, Annales Henri Poincare, 18, 3371, 10.1007/s00023-017-0592-z · DOI
  18. Barreto, 1997, Distribution of resonances for spherical black holes, Math. Res. Lett., 4, 103, 10.4310/mrl.1997.v4.n1.a10 · DOI
  19. Bony, 2008, Decay and non-decay of the local energy for the wave equation on the de Sitter–Schwarzschild metric, Commun. Math. Phys., 282, 697, 10.1007/s00220-008-0553-y · DOI
  20. Dyatlov, 2011, Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole, Commun. Math. Phys., 306, 119, 10.1007/s00220-011-1286-x · DOI
  21. Wunsch, 2011, Resolvent estimates for normally hyperbolic trapped sets, Ann. Henri Poincaré, 12, 1349, 10.1007/s00023-011-0108-1 · DOI
  22. Vasy, 2013, Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov), Invent. Math., 194, 381, 10.1007/s00222-012-0446-8 · DOI
  23. Dyatlov, 2016, Spectral gaps for normally hyperbolic trapping, Annales Inst. Fourier, 66, 55, 10.5802/aif.3005 · DOI
  24. Dyatlov, 2015, Resonance projectors and asymptotics for r-normally hyperbolic trapped sets, J. Am. Math. Soc., 28, 311, 10.1090/s0894-0347-2014-00822-5 · DOI
  25. Nonnenmacher, 2015, Decay of correlations for normally hyperbolic trapping, Invent. Math., 200, 345, 10.1007/s00222-014-0527-y · DOI
  26. Hintz, 2018, Asymptotics for the wave equation on differential forms on Kerr-de Sitter space, J. Diff. Geom., 110, 221, 10.4310/jdg/1538791244 · DOI
  27. Nollert, 1999, Quasinormal modes: the characteristic ‘sound’ of black holes and neutron stars, Class. Quantum Grav., 16, R159, 10.1088/0264-9381/16/12/201 · DOI
  28. Ori, 1991, Inner structure of a charged black hole: An exact mass-inflation solution, Phys. Rev. Lett., 67, 789, 10.1103/physrevlett.67.789 · DOI
  29. Cardoso, 2018, Quasinormal modes and Strong Cosmic Censorship, Phys. Rev. Lett., 120, 10.1103/PhysRevLett.120.031103 · DOI
  30. Luna, 2019, Strong Cosmic Censorship: the nonlinear story, Phys. Rev. D, 99, 10.1103/physrevd.99.064014 · DOI
  31. Hollands, 2001, Local Wick polynomials and time ordered products of quantum fields in curved space-time, Commun. Math. Phys., 223, 289, 10.1007/s002200100540 · DOI
  32. Sela, 2018, Quantum effects near the Cauchy horizon of a Reissner-Nordstr?m black hole, Phys. Rev. D, 98, 10.1103/physrevd.98.024025 · DOI
  33. Birrell, 1978, On falling through a black hole into another universe, Nature, 272, 35, 10.1038/272035a0 · DOI
  34. Marković, 1991, Vacuum for a massless scalar field outside a collapsing body in de Sitter space-time, Phys. Rev. D, 43, 332, 10.1103/physrevd.43.332 · DOI
  35. Dias, 2019, The BTZ black hole violates strong cosmic censorship, 10.1007/JHEP12(2019)097 · DOI · Paper page
  36. Tipler, 1977, Singularities in conformally flat spacetimes, Phys. Lett. A, 64, 8, 10.1016/0375-9601(77)90508-4 · DOI
  37. Hiscock, 1980, Quantum mechanical instability of the Kerr-Newman black hole interior, Phys. Rev. D, 21, 2057, 10.1103/physrevd.21.2057 · DOI
  38. Kay, 1992, The Principle of locality and quantum field theory on (nonglobally hyperbolic) curved space-times, Rev. Math. Phys., 4, 167, 10.1142/s0129055x92000194 · DOI
  39. Kay, 1991, Theorems on the Uniqueness and Thermal Properties of Stationary, Nonsingular, Quasifree States on Space-Times with a Bifurcate Killing Horizon, Phys. Rep., 207, 49, 10.1016/0370-1573(91)90015-e · DOI · Paper page
  40. Poisson, 2004, The Motion of point particles in curved space-time, Living Rev. Rel., 7, 6, 10.12942/lrr-2004-6 · DOI
  41. DeWitt, 1960, Radiation damping in a gravitational field, Ann. Phys., Lpz., 9, 220, 10.1016/0003-4916(60)90030-0 · DOI
  42. Hollands, 2002, Existence of local covariant time ordered products of quantum fields in curved space-time, Commun. Math. Phys., 231, 309, 10.1007/s00220-002-0719-y · DOI
  43. Hollands, 2010, Axiomatic quantum field theory in curved spacetime, Commun. Math. Phys., 293, 85, 10.1007/s00220-009-0880-7 · DOI
  44. Brunetti, 2003, The Generally covariant locality principle: A New paradigm for local quantum field theory, Commun. Math. Phys., 237, 31, 10.1007/s00220-003-0815-7 · DOI
  45. Radzikowski, 1996, Micro-local approach to the Hadamard condition in quantum field theory on curved space-time, Commun. Math. Phys., 179, 529, 10.1007/bf02100096 · DOI
  46. Brunetti, 2005, A Remark on alpha vacua for quantum field theories on de Sitter space, J. High Energy Phys., 10.1088/1126-6708/2005/05/063 · DOI
  47. Brunetti, 2000, Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds, Commun. Math. Phys., 208, 623, 10.1007/s002200050004 · DOI
  48. Radzikowski, 1996, A Local to global singularity theorem for quantum field theory on curved space-time, Commun. Math. Phys., 180, 1, 10.1007/bf02101180 · DOI
  49. Fulling, 1981, Singularity structure of the two point function in quantum field theory in curved space-time. II, Ann. Phys., Lpz., 136, 243, 10.1016/0003-4916(81)90098-1 · DOI
  50. Junker, 2002, Adiabatic vacuum states on general space-time manifolds: Definition, construction, and physical properties, Ann Henri Poincaré, 3, 1113, 10.1007/s000230200001 · DOI
  51. Gérard, 2014, Construction of Hadamard states by pseudo-differential calculus, Commun. Math. Phys., 325, 713, 10.1007/s00220-013-1824-9 · DOI
  52. Dappiaggi, 2011, Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime, Adv. Theor. Math. Phys., 15, 355, 10.4310/atmp.2011.v15.n2.a4 · DOI
  53. Dappiaggi, 2011, Local causal structures, Hadamard states and the principle of local covariance in quantum field theory, Commun. Math. Phys., 304, 459, 10.1007/s00220-011-1235-8 · DOI
  54. Duistermaat, 1972, Fourier integral operators. ii, Acta Math., 128, 183, 10.1007/bf02392165 · DOI
  55. Unruh, 1976, Notes on black hole evaporation, Phys. Rev. D, 14, 870, 10.1103/physrevd.14.870 · DOI · Paper page
  56. Dimock, 1980, Algebras of local observables on a manifold, Commun. Math. Phys., 77, 219, 10.1007/bf01269921 · DOI
  57. Verch, 1994, Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved space-time, Commun. Math. Phys., 160, 507, 10.1007/bf02173427 · DOI
  58. Kenig, 1993, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Commun. Pure Appl. Math., 46, 527, 10.1002/cpa.3160460405 · DOI
  59. Lanir, 2018, Two-point function of a quantum scalar field in the interior region of a Reissner-Nordstrom black hole, Phys. Rev. D, 97, 10.1103/physrevd.97.024033 · DOI
  60. Kehle, 2019, A Scattering Theory for Linear Waves on the Interior of Reissner-Nordström Black Holes, Annales Henri Poincare, 20, 1583, 10.1007/s00023-019-00760-z · DOI
  61. Suzuki, 1999, Analytic solutions of Teukolsky equation in Kerr-de Sitter and Kerr-Newman-de Sitter geometries, Prog. Theor. Phys., 102, 253, 10.1143/ptp.102.253 · DOI
  62. Schmidt, 1979, Die Lösung der linearen Differentialgleichung 2. Ordnung um zwei einfache Singularitäten durch Reihen nach hypergeometrischen Funktionen, J. Reine Angew. Math., 309, 127, 10.1515/crll.1979.309.127 · DOI
  63. Leaver, 1986, Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics, J. Math. Phys., 27, 1238, 10.1063/1.527130 · DOI
  64. Leaver, 1986, Spectral decomposition of the perturbation response of the Schwarzschild geometry, Phys. Rev. D, 34, 384, 10.1103/physrevd.34.384 · DOI
  65. Gautschi, 1967, Computational aspects of three-term recurrence relations, SIAM Rev., 9, 24, 10.1137/1009002 · DOI
  66. Banados, 1992, The Black hole in three-dimensional space-time, Phys. Rev. Lett., 69, 1849, 10.1103/physrevlett.69.1849 · DOI · Paper page
  67. Banados, 1993, Geometry of the (2+1) black hole, Phys. Rev. D, 48, 1506, 10.1103/physrevd.48.1506 · DOI · Paper page
  68. Banados, 2013, Geometry of the (2+1) black hole, Phys. Rev. D, 88, 10.1103/physrevd.88.069902 · DOI

Cited by

Sorted by citations

Metadata

Authors
Hollands, S., Wald, R. M., & Zahn, J.
ORCID
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
2020-05-12
Volume
37
Issue
11
Pages
115009
ISSN
  • 0264-9381
  • 1361-6382
DOI
10.1088/1361-6382/ab8052
Cited by
125
References
3
Licence
Funders
  • National Science Foundation (PHY18-04216)
  • Max-Planck-Gesellschaft (M.FE.A.MATN0003)

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review