CoChat
Sign Up
Cited by 60

The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.

The BTZ black hole violates strong cosmic censorship

Dias, Oscar J.C., Reall, Harvey S., Santos, Jorge E.·2019·Journal of High Energy Physics
DOI 10.1007/jhep12(2019)097
Open this paper in CoChat — free account

Abstract

We investigate the stability of the inner horizon of a rotating BTZ black hole. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. This is demonstrated for scalar fields, for massive Chern-Simons fields, for Proca fields, and for massive spin-2 fields. Thus the strong cosmic censorship conjecture is violated by a near-extremal BTZ black hole in a large class of theories. However, we show that a weaker \rough" version of the conjecture is respected. We calculate the renormalized energymomentum tensor of a scalar field in the Hartle-Hawking state in the BTZ geometry. We show that the result is finite at the inner horizon of a near-extremal black hole. Hence the backreaction of vacuum polarization does not enforce strong cosmic censorship.

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 · 10.1007/jhep12(2019)097

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Figures

Figure 1 Penrose diagram for the non-extremal BTZ black hole. Region I is the black hole exterior and region II the interior. The asymptotic timelike boundary is I R , the future event horizon is H + R and the past event horizon is at H -R . Region III is the white hole region. Region IV is another asymptotically AdS region with timelike boundary I L and future event horizon H + L . CH + L,R are the 'left' and 'right' future Cauchy horizons, respectively.
Figure 1 Penrose diagram for the non-extremal BTZ black hole. Region I is the black hole exterior and region II the interior. The asymptotic timelike boundary is I R , the future event horizon is H + R and the past event horizon is at H -R . Region III is the white hole region. Region IV is another asymptotically AdS region with timelike boundary I L and future event horizon H + L . CH + L,R are the 'left' and 'right' future Cauchy horizons, respectively.CC-BY · From the PDF
Figure 2 The conformal dimension ∆ as a function of the scalar field mass µ 2 L 2 . The upper branch (blue) corresponds to ∆ + , the lower branch (orange) to ∆ -. Note ∆ ± ( µ BF ) = 1 and ∆ -(0) = 0.
Figure 2 The conformal dimension ∆ as a function of the scalar field mass µ 2 L 2 . The upper branch (blue) corresponds to ∆ + , the lower branch (orange) to ∆ -. Note ∆ ± ( µ BF ) = 1 and ∆ -(0) = 0.CC-BY · From the PDF
Figure 3 Our (characteristic) initial-boundary data for solving the Klein-Gordon equation consists of smooth (outgoing) wavepackets on H + L and H -R and a smooth wavepacket source at I R . We will determine the solution in regions I and II and investigate its smoothness at CH + R .
Figure 3 Our (characteristic) initial-boundary data for solving the Klein-Gordon equation consists of smooth (outgoing) wavepackets on H + L and H -R and a smooth wavepacket source at I R . We will determine the solution in regions I and II and investigate its smoothness at CH + R .CC-BY · From the PDF
Figure 4 Contours of integration C and C m in the complex ω plane and the relevant poles: poles marked in red contribute to the integral and poles marked in black don't. The pole with smallest | Im( ω ) | on the left is the fundamental retrograde quasinormal mode ϖ m and on the right we show the poles with ω -m Ω -= -inκ -which only give a smooth contribution at CH + R .
Figure 4 Contours of integration C and C m in the complex ω plane and the relevant poles: poles marked in red contribute to the integral and poles marked in black don't. The pole with smallest | Im( ω ) | on the left is the fundamental retrograde quasinormal mode ϖ m and on the right we show the poles with ω -m Ω -= -inκ -which only give a smooth contribution at CH + R .CC-BY · From the PDF
Figure 5 Plot of L 3 〈 0 | T rr | 0 〉 as a function of log 10 ( ζ -χ ) computed for ∆ = 1, α = 2 π and β = 3 / 2. The black dot denotes L 3 t rr .
Figure 5 Plot of L 3 〈 0 | T rr | 0 〉 as a function of log 10 ( ζ -χ ) computed for ∆ = 1, α = 2 π and β = 3 / 2. The black dot denotes L 3 t rr .CC-BY · From the PDF
Figure 6 Left panel: Logarithmic plot of L 3 t rr as a function of β . Right panel: L 3 ( β -1) t rr as a function of β . Both plots are for ∆ = 2 and α = 2 π . The vertical red dashed line marks β = 1. The plots show that lim r → r -〈 0 | T rr | 0 〉 diverges as 1 / ( β -1) as β → 1 + .
Figure 6 Left panel: Logarithmic plot of L 3 t rr as a function of β . Right panel: L 3 ( β -1) t rr as a function of β . Both plots are for ∆ = 2 and α = 2 π . The vertical red dashed line marks β = 1. The plots show that lim r → r -〈 0 | T rr | 0 〉 diverges as 1 / ( β -1) as β → 1 + .CC-BY · From the PDF
Figure 7 Left panel: Plot of ( ζ -χ ) 1 -β L 3 〈 0 | T rr | 0 〉 as a function of log 10 ( ζ -χ ) showing the complete range of ζ that we probed. Right panel: Plot of ( ζ -χ ) 1 -β L 3 〈 0 | T rr | 0 〉 in the range -200 < log 10 ( ζ -χ ) < -180 corresponding to the orange region on the left panel. Both panels are for ∆ = 1, β = 1 / 2 and α = 2 π .
Figure 7 Left panel: Plot of ( ζ -χ ) 1 -β L 3 〈 0 | T rr | 0 〉 as a function of log 10 ( ζ -χ ) showing the complete range of ζ that we probed. Right panel: Plot of ( ζ -χ ) 1 -β L 3 〈 0 | T rr | 0 〉 in the range -200 < log 10 ( ζ -χ ) < -180 corresponding to the orange region on the left panel. Both panels are for ∆ = 1, β = 1 / 2 and α = 2 π .CC-BY · From the PDF
Figure 8 Left panel: | σ N | computed for several values of N . Right panel: | ( β -N ) σ N | as a function of β computed for several values of N . In both panels, the solid blue curve corresponds to N = 1, the orange dashed line to N = 2 and the dotted green line to N = 3. Finally, the vertical lines represent β = 1 , 2 , 3, from left to right. In all cases we fixed α = 2 π .
Figure 8 Left panel: | σ N | computed for several values of N . Right panel: | ( β -N ) σ N | as a function of β computed for several values of N . In both panels, the solid blue curve corresponds to N = 1, the orange dashed line to N = 2 and the dotted green line to N = 3. Finally, the vertical lines represent β = 1 , 2 , 3, from left to right. In all cases we fixed α = 2 π .CC-BY · From the PDF
Figure 9 Left panel: | Ξ N ( r ) | + N -1 , computed for several values of N , as a function of log 10 ( ζ -χ ). The N -1 offset has been added to prevent the curves lying on top of each other. Right panel: ∣ ∣ ∣ Ξ N ( r ) -Ξ N ( r ) ∣ ∣ ∣ in the region -190 < log 10 ( ζ -χ ) < -185, corresponding to the red band on the left panel. In both panels, the blue disks corresponds to N = 1, the orange squares to N = 2 and the green diamonds to N = 3. In all cases we we have α = 2 π and β = 1 / 2.
Figure 9 Left panel: | Ξ N ( r ) | + N -1 , computed for several values of N , as a function of log 10 ( ζ -χ ). The N -1 offset has been added to prevent the curves lying on top of each other. Right panel: ∣ ∣ ∣ Ξ N ( r ) -Ξ N ( r ) ∣ ∣ ∣ in the region -190 < log 10 ( ζ -χ ) < -185, corresponding to the red band on the left panel. In both panels, the blue disks corresponds to N = 1, the orange squares to N = 2 and the green diamonds to N = 3. In all cases we we have α = 2 π and β = 1 / 2.CC-BY · From the PDF

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?

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

Show all 1 references

Research works printed but not linked: 49

  1. M. Simpson and R. Penrose, Internal instability in a Reissner-Nordstrom black hole, Int. J. Theor. Phys.7 (1973) 183 [INSPIRE]. · DOI · Paper page
  2. J. McNamara, Instability of black hole inner horizons, Proc. Roy. Soc. LondonA 358 (1978) 499. · DOI
  3. S. Chandrasekhar and J.B. Hartle, On crossing the cauchy horizon of a Reissner-Nordstr¨om black-hole, Proc. Roy. Soc. LondonA 384 (1982) 301. · DOI
  4. E. Poisson and W. Israel, Internal structure of black holes, Phys. Rev.D 41 (1990) 1796 [INSPIRE].
  5. M. Dafermos, The interior of charged black holes and the problem of uniqueness in general relativity, Commun. Pure Appl. Math.58 (2005) 0445 [gr-qc/0307013] [INSPIRE]. · DOI
  6. A. Ori, Inner structure of a charged black hole: an exact mass-inflation solution, Phys. Rev. Lett.67 (1991) 789 [INSPIRE]. · DOI
  7. M. Dafermos and J. Luk, The interior of dynamical vacuum black holes I: the C 0-stability of the Kerr Cauchy horizon, arXiv:1710.01722 [INSPIRE]. · arXiv
  8. J. Luk and S.-J. Oh, Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data I. The interior of the black hole region, arXiv:1702.05715 [INSPIRE]. · arXiv
  9. M. Dafermos, Black holes without spacelike singularities, Commun. Math. Phys.332 (2014) 729 [arXiv:1201.1797] [INSPIRE]. · DOI
  10. R. Penrose, Singularities of spacetime, in Theoretical principles in astrophysics and relativity, N.R. Liebowitz and P.O. Vandervoort eds., Chicago University Press, Chicago U.S.A. (1978).
  11. V. Cardoso et al., Quasinormal modes and strong cosmic censorship, Phys. Rev. Lett.120 (2018) 031103 [arXiv:1711.10502] [INSPIRE]. · DOI
  12. O.J.C. Dias, H.S. Reall and J.E. Santos, Strong cosmic censorship: taking the rough with the smooth, JHEP10 (2018) 001 [arXiv:1808.02895] [INSPIRE]. · DOI
  13. R. Luna et al., Strong cosmic censorship: the nonlinear story, Phys. Rev.D 99 (2019) 064014 [arXiv:1810.00886] [INSPIRE]. · arXiv
  14. F. Mellor and I. Moss, Stability of black holes in de Sitter space, Phys. Rev.D 41 (1990) 403 [INSPIRE].
  15. O.J.C. Dias, F.C. Eperon, H.S. Reall and J.E. Santos, Strong cosmic censorship in de Sitter space, Phys. Rev.D 97 (2018) 104060 [arXiv:1801.09694] [INSPIRE]. · arXiv
  16. G. Festuccia and H. Liu, A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, Adv. Sci. Lett.2 (2009) 221 [arXiv:0811.1033] [INSPIRE]. · DOI
  17. G. Holzegel and J. Smulevici, Decay properties of Klein-Gordon fields on Kerr-AdS spacetimes, Commun. Pure Appl. Math.66 (2013) 1751 [arXiv:1110.6794] [INSPIRE]. · DOI
  18. C. Kehle, Uniform boundedness and continuity at the Cauchy horizon for linear waves on Reissner-Nordstr¨om-AdS black holes, arXiv:1812.06142 [INSPIRE]. · arXiv
  19. S. Bhattacharjee, S. Sarkar and A. Virmani, Internal structure of charged AdS black holes, Phys. Rev.D 93 (2016) 124029 [arXiv:1604.03730] [INSPIRE]. · arXiv
  20. M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett.69 (1992) 1849 [hep-th/9204099] [INSPIRE]. · DOI · Paper page
  21. M. Bañdos, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2+ 1) black hole, Phys. Rev.D 48 (1993) 1506 [Erratum ibid.D 88 (2013) 069902] [gr-qc/9302012] [INSPIRE]. · DOI · Paper page
  22. O. Aharony et al., Large N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE]. · DOI
  23. D. Birmingham, Choptuik scaling and quasinormal modes in the AdS/CFT correspondence, Phys. Rev.D 64 (2001) 064024 [hep-th/0101194] [INSPIRE]. · arXiv
  24. M. Dafermos and Y. Shlapentokh-Rothman, Rough initial data and the strength of the blue-shift instability on cosmological black holes with Λ < 0, Class. Quant. Grav.35 (2018) 195010 [arXiv:1805.08764] [INSPIRE]. · DOI
  25. N.D. Birrell and P.C.W. Davies, On falling through a black hole into another universe, Nature272 (1978) 35 [INSPIRE]. · DOI
  26. V. Balasubramanian and T.S. Levi, Beyond the veil: inner horizon instability and holography, Phys. Rev.D 70 (2004) 106005 [hep-th/0405048] [INSPIRE]. · arXiv
  27. A.R. Steif, The quantum stress tensor in the three-dimensional black hole, Phys. Rev.D 49 (1994) 585 [gr-qc/9308032] [INSPIRE]. · DOI · Paper page
  28. P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys.144 (1982) 249 [INSPIRE]. · DOI · Paper page
  29. L. Mezincescu and P.K. Townsend, Stability at a local maximum in higher dimensional Anti-de Sitter space and applications to supergravity, Annals Phys.160 (1985) 406 [INSPIRE]. · DOI
  30. I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys.B 556 (1999) 89 [hep-th/9905104] [INSPIRE]. · DOI
  31. P. Hintz and A. Vasy, Analysis of linear waves near the Cauchy horizon of cosmological black holes, J. Math. Phys.58 (2017) 081509 [arXiv:1512.08004] [INSPIRE]. · DOI
  32. M. Abramowitz and I. Stegun, Handbook of mathematical functions, Dover, New York U.S.A. (1964).
  33. C. Kehle and Y. Shlapentokh-Rothman, A scattering theory for linear waves on the interior of Reissner–Nordstr¨om black holes, Ann. Henri Poincaŕe20 (2019) 1583 [arXiv:1804.05438] [INSPIRE]. · DOI
  34. D. Christodoulou, The formation of black holes in general relativity, European Mathematical Society, Poland (2009). · DOI
  35. E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE]. · arXiv
  36. A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett.B 379 (1996) 99 [hep-th/9601029] [INSPIRE]. · DOI · Paper page
  37. J.P. Gauntlett, O.A.P. Mac Conamhna, T. Mateos and D. Waldram, Supersymmetric AdS 3solutions of type IIB supergravity, Phys. Rev. Lett.97 (2006) 171601 [hep-th/0606221] [INSPIRE]. · DOI
  38. T. Andrade, J.I. Jottar and R.G. Leigh, Boundary conditions and unitarity: the Maxwell-Chern-Simons system in AdS 3/C F T 2 , JHEP05 (2012) 071 [arXiv:1111.5054] [INSPIRE]. · DOI
  39. W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP04 (2008) 082 [arXiv:0801.4566] [INSPIRE]. · DOI
  40. Y. Liu and Y.-w. Sun, Note on new massive gravity in AdS 3 , JHEP04 (2009) 106 [arXiv:0903.0536] [INSPIRE]. · DOI
  41. M. Casals, A. Fabbri, C. Martínez and J. Zanelli, Quantum backreaction on three-dimensional black holes and naked singularities, Phys. Rev. Lett.118 (2017) 131102 [arXiv:1608.05366] [INSPIRE]. · DOI
  42. M. Casals, A. Fabbri, C. Martínez and J. Zanelli, Quantum-corrected rotating black holes and naked singularities in (2+ 1) dimensions, Phys. Rev.D 99 (2019) 104023 [arXiv:1902.01583] [INSPIRE]. · DOI · Paper page
  43. R.M. Wald, Quantum field theory in curved space-time and black hole thermodynamics, Chicago Lectures in Physics. University of Chicago Press, Chicago U.S.A. (1995).
  44. Y. Decanini and A. Folacci, Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension, Phys. Rev.D 78 (2008) 044025 [gr-qc/0512118] [INSPIRE]. · DOI
  45. R.M. Wald, The back reaction effect in particle creation in curved space-time, Commun. Math. Phys.54 (1977) 1 [INSPIRE]. · DOI · Paper page
  46. S. Hollands and R.M. Wald, Local Wick polynomials and time ordered products of quantum fields in curved space-time, Commun. Math. Phys.223 (2001) 289 [gr-qc/0103074] [INSPIRE]. · DOI
  47. I. Ichinose and Y. Satoh, Entropies of scalar fields on three-dimensional black holes, Nucl. Phys.B 447 (1995) 340 [hep-th/9412144] [INSPIRE]. · DOI
  48. A. Lanir, A. Ori, N. Zilberman, O. Sela, A. Maline and A. Levi, Analysis of quantum effects inside spherical charged black holes, Phys. Rev.D 99 (2019) 061502 [arXiv:1811.03672] [INSPIRE]. · arXiv
  49. V.E. Hubeny, D. Marolf and M. Rangamani, Hawking radiation from AdS black holes, Class. Quant. Grav.27 (2010) 095018 [arXiv:0911.4144] [INSPIRE]. · DOI · Paper page

Cited by

Sorted by citations

Metadata

Authors
Dias, O. J. C., Reall, H. S., & Santos, J. E.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2019-12
Volume
2019
Issue
12
ISSN
1029-8479
DOI
10.1007/jhep12(2019)097
Cited by
60
References
1
Language
en
Licence

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