Abstract
We compute the quasi-normal frequencies of scalars in asymptotically-flat microstate geometries that have the same charge as a D1-D5-P black hole, but whose long BTZ-like throat ends in a smooth cap. In general the wave equation is not separable, but we find a class of geometries in which the non-separable term is negligible and we can compute the quasi-normal frequencies using WKB methods. We argue that our results are a universal property of all microstate geometries with deeply-capped BTZ throats. These throats generate large redshifts, which lead to exceptionally-low-energy states with extremely long decay times, set by the central charge of the dual CFT to the power of twice the dimension of the operator dual to the mode. While these decay times are extremely long, we also argue that the energy decay is bounded, at large t, by (log(t))−2 and is comparable with the behavior of ultracompact stars, as one should expect for microstate geometries.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I. Bena, C.-W. Wang and N.P. Warner, Mergers and typical black hole microstates, JHEP 11 (2006) 042 [hep-th/0608217] [INSPIRE].
I. Bena, C.-W. Wang and N.P. Warner, Plumbing the Abyss: Black ring microstates, JHEP 07 (2008) 019 [arXiv:0706.3786] [INSPIRE].
I. Bena et al., Smooth horizonless geometries deep inside the black-hole regime, Phys. Rev. Lett. 117 (2016) 201601 [arXiv:1607.03908] [INSPIRE].
I. Bena et al., Asymptotically-fiat super-gravity solutions deep inside the black-hole regime, JHEP 02 (2018) 014 [arXiv:1711.10474] [INSPIRE].
P. Heidmann, Four-center bubbled BPS solutions with a Gibbons-Hawking base, JHEP 10 (2017) 009 [arXiv:1703.10095] [INSPIRE].
I. Bena, P. Heidmann and P.F. Ramirez, A systematic construction of microstate geometries with low angular momentum, JHEP 10 (2017) 217 [arXiv:1709.02812] [INSPIRE].
J. Avila, P.F. Ramirez and A. Ruiperez, One Thousand and One Bubbles, JHEP 01 (2018) 041 [arXiv:1709.03985] [INSPIRE].
N. Čeplak, R. Russo and M. Shigemori, Supercharging Superstrata, JHEP 03 (2019) 095 [arXiv:1812.08761] [INSPIRE].
P. Heidmann and N.P. Warner, Superstratum Symbiosis, JHEP 09 (2019) 059 [arXiv:1903.07631] [INSPIRE].
P. Heidmann, D.R. Mayerson, R. Walker and N.P. Warner, Holomorphic Waves of Black Hole Microstructure, JHEP 02 (2020) 192 [arXiv:1910.10714] [INSPIRE].
A. Tyukov, R. Walker and N.P. Warner, Tidal Stresses and Energy Gaps in Microstate Geometries, JHEP 02 (2018) 122 [arXiv:1710.09006] [INSPIRE].
I. Bena, E.J. Martinec, R. Walker and N.P. Warner, Early Scrambling and Capped BTZ Geometries, JHEP 04 (2019) 126 [arXiv:1812.05110] [INSPIRE].
I. Bena, P. Heidmann and D. Turton, AdS2 holography: mind the cap, JHEP 12 (2018) 028 [arXiv:1806.02834] [INSPIRE].
I. Bena, P. Heidmann, R. Monten and N.P. Warner, Thermal Decay without Information Loss in Horizonless Microstate Geometries, SciPost Phys. 7 (2019) 063 [arXiv:1905.05194] [INSPIRE].
V. Cardoso, O.J.C. Dias, J.L. Hovdebo and R.C. Myers, Instability of non-supersymmetric smooth geometries, Phys. Rev. D 73 (2006) 064031 [hep-th/0512277] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Radiation from the non-extremal fuzzball, Class. Quant. Grav. 25 (2008) 135005 [arXiv:0711.4817] [INSPIRE].
B. Chakrabarty, D. Turton and A. Virmani, Holographic description of non-supersymmetric orbifolded D1-D5-P solutions, JHEP 11 (2015) 063 [arXiv:1508.01231] [INSPIRE].
F.C. Eperon, H.S. Reall and J.E. Santos, Instability of supersymmetric microstate geometries, JHEP 10 (2016) 031 [arXiv:1607.06828] [INSPIRE].
B. Chakrabarty, D. Ghosh and A. Virmani, Quasinormal modes of supersymmetric microstate geometries from the D1-D5 CFT, JHEP 10 (2019) 072 [arXiv:1908.01461] [INSPIRE].
J. Keir, Wave propagation on microstate geometries, Annales Henri Poincaré 21 (2019) 705 [arXiv:1609.01733] [INSPIRE].
F.C. Eperon, Geodesics in supersymmetric microstate geometries, Class. Quant. Grav. 34 (2017) 165003 [arXiv:1702.03975] [INSPIRE].
J. Keir, Evanescent ergosurface instability, Anal. Part. Diff. Eq. 13 (2020) 1833 [arXiv:1810.03026] [INSPIRE].
V.S. Rychkov, D1-D5 black hole microstate counting from supergravity, JHEP 01 (2006) 063 [hep-th/0512053] [INSPIRE].
I. Bena, M. Shigemori and N.P. Warner, Black-Hole Entropy from Supergravity Superstrata States, JHEP 10 (2014) 140 [arXiv:1406.4506] [INSPIRE].
D. Marolf, B. Michel and A. Puhm, A rough end for smooth microstate geometries, JHEP 05 (2017) 021 [arXiv:1612.05235] [INSPIRE].
S. Giusto, S.D. Mathur and A. Saxena, Dual geometries for a set of 3-charge microstates, Nucl. Phys. B 701 (2004) 357 [hep-th/0405017] [INSPIRE].
S. Giusto, S.D. Mathur and A. Saxena, 3-charge geometries and their CFT duals, Nucl. Phys. B 710 (2005) 425 [hep-th/0406103] [INSPIRE].
S. Giusto and S.D. Mathur, Geometry of D1-D5-P bound states, Nucl. Phys. B 729 (2005) 203 [hep-th/0409067] [INSPIRE].
S. Giusto, O. Lunin, S.D. Mathur and D. Turton, D1-D5-P microstates at the cap, JHEP 02 (2013) 050 [arXiv:1211.0306] [INSPIRE].
V. Jejjala, O. Madden, S.F. Ross and G. Titchener, Non-supersymmetric smooth geometries and D1-D5-P bound states, Phys. Rev. D 71 (2005) 124030 [hep-th/0504181] [INSPIRE].
O. Lunin and S.D. Mathur, Metric of the multiply wound rotating string, Nucl. Phys. B 610 (2001) 49 [hep-th/0105136] [INSPIRE].
O. Lunin and S.D. Mathur, The Slowly rotating near extremal D1-D5 system as a ‘hot tube’, Nucl. Phys. B 615 (2001) 285 [hep-th/0107113] [INSPIRE].
I. Bena, S. Giusto, R. Russo, M. Shigemori and N.P. Warner, Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP 05 (2015) 110 [arXiv:1503.01463] [INSPIRE].
A.W. Peet, TASI lectures on black holes in string theory, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 99): Strings, Branes, and Gravity, (2000) [DOI] [hep-th/0008241] [INSPIRE].
S. Iyer and C.M. Will, Black Hole Normal Modes: A WKB Approach. 1. Foundations and Application of a Higher Order WKB Analysis of Potential Barrier Scattering, Phys. Rev. D 35 (1987) 3621 [INSPIRE].
I. Bena, D. Turton, R. Walker and N.P. Warner, Integrability and Black-Hole Microstate Geometries, JHEP 11 (2017) 021 [arXiv:1709.01107] [INSPIRE].
R. Walker, D1-D5-P superstrata in 5 and 6 dimensions: separable wave equations and prepotentials, JHEP 09 (2019) 117 [arXiv:1906.04200] [INSPIRE].
S. Raju and P. Shrivastava, Critique of the fuzzball program, Phys. Rev. D 99 (2019) 066009 [arXiv:1804.10616] [INSPIRE].
M. Shigemori, Superstrata, Gen. Rel. Grav. 52 (2020) 51 [arXiv:2002.01592] [INSPIRE].
J.B. Gutowski, D. Martelli and H.S. Reall, All Supersymmetric solutions of minimal supergravity in six- dimensions, Class. Quant. Grav. 20 (2003) 5049 [hep-th/0306235] [INSPIRE].
M. Cariglia and O.A.P. Mac Conamhna, The General form of supersymmetric solutions of N = (1, 0) U(1) and SU(2) gauged supergravities in six-dimensions, Class. Quant. Grav. 21 (2004) 3171 [hep-th/0402055] [INSPIRE].
O. Lunin, Adding momentum to D1-D5 system, JHEP 04 (2004) 054 [hep-th/0404006] [INSPIRE].
J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, Quantizing N = 2 Multicenter Solutions, JHEP 05 (2009) 002 [arXiv:0807.4556] [INSPIRE].
J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, A Bound on the entropy of supergravity?, JHEP 02 (2010) 062 [arXiv:0906.0011] [INSPIRE].
G. Holzegel and J. Smulevici, Quasimodes and a lower bound on the uniform energy decay rate for Kerr-AdS spacetimes, Anal. Part. Diff. Eq. 7 (2014) 1057 [arXiv:1303.5944] [INSPIRE].
J. Keir, Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars, Class. Quant. Grav. 33 (2016) 135009 [arXiv:1404.7036] [INSPIRE].
V. Cardoso, L.C.B. Crispino, C.F.B. Macedo, H. Okawa and P. Pani, Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects, Phys. Rev. D 90 (2014) 044069 [arXiv:1406.5510] [INSPIRE].
G. Moschidis, Logarithmic local energy decay for scalar waves on a general class of asymptotically flat spacetimes, arXiv:1509.08495 [INSPIRE].
V. Cardoso, E. Franzin and P. Pani, Is the gravitational-wave ringdown a probe of the event horizon?, Phys. Rev. Lett. 116 (2016) 171101 [Erratum ibid. 117 (2016) 089902] [arXiv:1602.07309] [INSPIRE].
V. Cardoso and P. Pani, Testing the nature of dark compact objects: a status report, Living Rev. Rel. 22 (2019) 4 [arXiv:1904.05363] [INSPIRE].
I. Bena, A. Puhm and B. Vercnocke, Metastable Supertubes and non-extremal Black Hole Microstates, JHEP 04 (2012) 100 [arXiv:1109.5180] [INSPIRE].
I. Bena, A. Puhm and B. Vercnocke, Non-extremal Black Hole Microstates: Fuzzballs of Fire or Fuzzballs of Fuzz?, JHEP 12 (2012) 014 [arXiv:1208.3468] [INSPIRE].
S. Kachru, J. Pearson and H.L. Verlinde, Brane/flux annihilation and the string dual of a nonsupersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [INSPIRE].
I. Bena, D.R. Mayerson, A. Puhm and B. Vercnocke, Tunneling into Microstate Geometries: Quantum Effects Stop Gravitational Collapse, JHEP 07 (2016) 031 [arXiv:1512.05376] [INSPIRE].
D.R. Mayerson, R.A. Walker and N.P. Warner, Microstate Geometries from Gauged Supergravity in Three Dimensions, JHEP 10 (2020) 030 [arXiv:2004.13031] [INSPIRE].
I. Bena, E. Martinec, D. Turton and N.P. Warner, Momentum Fractionation on Superstrata, JHEP 05 (2016) 064 [arXiv:1601.05805] [INSPIRE].
S. Giusto, E. Moscato and R. Russo, AdS3 holography for 1/4 and 1/8 BPS geometries, JHEP 11 (2015) 004 [arXiv:1507.00945] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Pair creation in non-extremal fuzzball geometries, Class. Quant. Grav. 25 (2008) 225021 [arXiv:0806.2309] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Non-extremal fuzzballs and ergoregion emission, Class. Quant. Grav. 26 (2009) 035006 [arXiv:0810.2951] [INSPIRE].
S.G. Avery, B.D. Chowdhury and S.D. Mathur, Emission from the D1D5 CFT, JHEP 10 (2009) 065 [arXiv:0906.2015] [INSPIRE].
T.J.M. Zouros and D.M. Eardley, Instabilities of massive scalar perturbations of a rotating black hole, Annals Phys. 118 (1979) 139 [INSPIRE].
R.A. Konoplya and A. Zhidenko, Quasinormal modes of black holes: From astrophysics to string theory, Rev. Mod. Phys. 83 (2011) 793 [arXiv:1102.4014] [INSPIRE].
R.A. Konoplya, A. Zhidenko and A.F. Zinhailo, Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations, Class. Quant. Grav. 36 (2019) 155002 [arXiv:1904.10333] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2005.11323
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Bena, I., Eperon, F., Heidmann, P. et al. The great escape: tunneling out of microstate geometries. J. High Energ. Phys. 2021, 112 (2021). https://doi.org/10.1007/JHEP04(2021)112
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)112