Abstract
We use families of circular null geodesics as probes of a family of microstate geometries, known as (1, 0, n) superstrata. These geometries carry a left-moving momentum wave and the behavior of some of the geodesic probes is very sensitive to this background wave. The left-moving geodesics behave like BPS particles and so can be placed in circular orbits anywhere in the geometry and actually “float” at fixed radius and angle in the three-dimensional “capped BTZ” geometry. The right-moving geodesics behave like non-BPS particles. We show that they provide a simple geometric characterization of the black-hole bound: when the momentum charge of the geometry is below this bound, such geodesics can be placed anywhere, but exceeding the bound, even by a small amount, means these geodesics are restricted to the deep interior of the geometry. We also show that for left-moving string probes, the tidal forces remain comparable with those of global AdS3. Nevertheless, for some of these probes, the “bumps” in the geometry induce an oscillatory mass term and we discuss how this can lead to chaotic scrambling of the state of the string.
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References
R. Penrose, Techniques in Differential Topology in Relativity, Society for Industrial and Applied Mathematics (1972) [https://doi.org/10.1137/1.9781611970609].
R. Penrose, Any space-time has a plane wave as a limit, in Differential Geometry and Relativity, M. Cahen and M. Flato eds., D. Reidel Publishing, Dordrecht, Netherlands (1976) [https://doi.org/10.1007/978-94-010-1508-0].
R. Gueven, Plane wave limits and T duality, Phys. Lett. B 482 (2000) 255 [hep-th/0005061] [INSPIRE].
G.T. Horowitz and A.R. Steif, Strings in Strong Gravitational Fields, Phys. Rev. D 42 (1990) 1950 [INSPIRE].
M. Blau, J.M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, Penrose limits and maximal supersymmetry, Class. Quant. Grav. 19 (2002) L87 [hep-th/0201081] [INSPIRE].
M. Blau, J.M. Figueroa-O’Farrill and G. Papadopoulos, Penrose limits, supergravity and brane dynamics, Class. Quant. Grav. 19 (2002) 4753 [hep-th/0202111] [INSPIRE].
M. Blau, M. Borunda, M. O’Loughlin and G. Papadopoulos, Penrose limits and space-time singularities, Class. Quant. Grav. 21 (2004) L43 [hep-th/0312029] [INSPIRE].
M. Blau, M. Borunda, M. O’Loughlin and G. Papadopoulos, The Universality of Penrose limits near space-time singularities, JHEP 07 (2004) 068 [hep-th/0403252] [INSPIRE].
M. Blau, D. Frank and S. Weiss, Fermi coordinates and Penrose limits, Class. Quant. Grav. 23 (2006) 3993 [hep-th/0603109] [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, A. Houppe and N.P. Warner, Delaying the Inevitable: Tidal Disruption in Microstate Geometries, JHEP 02 (2021) 103 [arXiv:2006.13939] [INSPIRE].
E.J. Martinec and N.P. Warner, The Harder They Fall, the Bigger They Become: Tidal Trapping of Strings by Microstate Geometries, JHEP 04 (2021) 259 [arXiv:2009.07847] [INSPIRE].
N. Ceplak, S. Hampton and Y. Li, Toroidal tidal effects in microstate geometries, JHEP 03 (2022) 021 [arXiv:2106.03841] [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].
D. Marolf, B. Michel and A. Puhm, A rough end for smooth microstate geometries, JHEP 05 (2017) 021 [arXiv:1612.05235] [INSPIRE].
I. Bena, F. Eperon, P. Heidmann and N.P. Warner, The Great Escape: Tunneling out of Microstate Geometries, JHEP 04 (2021) 112 [arXiv:2005.11323] [INSPIRE].
G.W. Gibbons and N.P. Warner, Global structure of five-dimensional fuzzballs, Class. Quant. Grav. 31 (2014) 025016 [arXiv:1305.0957] [INSPIRE].
I. Bena, C.-W. Wang and N.P. Warner, Black rings with varying charge density, JHEP 03 (2006) 015 [hep-th/0411072] [INSPIRE].
G.T. Horowitz and H.S. Reall, How hairy can a black ring be?, Class. Quant. Grav. 22 (2005) 1289 [hep-th/0411268] [INSPIRE].
I. Bena, S.F. Ross and N.P. Warner, Coiffured Black Rings, Class. Quant. Grav. 31 (2014) 165015 [arXiv:1405.5217] [INSPIRE].
D. Berenstein, E. Maderazo, R. Mancilla and A. Ramirez, Chaotic LLM billiards, arXiv:2305.19321 [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, D. Turton, R. Walker and N.P. Warner, Integrability and Black-Hole Microstate Geometries, JHEP 11 (2017) 021 [arXiv:1709.01107] [INSPIRE].
I. Bena et al., Asymptotically-flat supergravity solutions deep inside the black-hole regime, JHEP 02 (2018) 014 [arXiv:1711.10474] [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].
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].
S. Giusto, L. Martucci, M. Petrini and R. Russo, 6D microstate geometries from 10D structures, Nucl. Phys. B 876 (2013) 509 [arXiv:1306.1745] [INSPIRE].
I. Bena et al., Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP 05 (2015) 110 [arXiv:1503.01463] [INSPIRE].
I. Bena, S. Giusto, C. Ruef and N.P. Warner, Supergravity Solutions from Floating Branes, JHEP 03 (2010) 047 [arXiv:0910.1860] [INSPIRE].
B. Ganchev, A. Houppe and N.P. Warner, Q-balls meet fuzzballs: non-BPS microstate geometries, JHEP 11 (2021) 028 [arXiv:2107.09677] [INSPIRE].
B. Ganchev, A. Houppe and N.P. Warner, New superstrata from three-dimensional supergravity, JHEP 04 (2022) 065 [arXiv:2110.02961] [INSPIRE].
B. Ganchev, A. Houppe and N.P. Warner, Elliptical and purely NS superstrata, JHEP 09 (2022) 067 [arXiv:2207.04060] [INSPIRE].
B. Ganchev et al., Microstrata, JHEP 10 (2023) 163 [arXiv:2307.13021] [INSPIRE].
Acknowledgments
We are grateful for valuable conversations with Iosif Bena, Nejc Čeplak, Bogdan Ganchev, Anthony Houppe and Rodolfo Russo. The work of NPW is supported in part by the DOE grant DE-SC0011687. The work of BG and NPW is supported in part by the ERC Grant 787320 — QBH Structure. The work of SDH is supported by ERC Grant 787320 — QBH Structure and by KIAS Grant PG096301.
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Guo, B., Hampton, S.D. & Warner, N.P. Inscribing geodesic circles on the face of the superstratum. J. High Energ. Phys. 2024, 224 (2024). https://doi.org/10.1007/JHEP05(2024)224
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DOI: https://doi.org/10.1007/JHEP05(2024)224