TY - JOUR

T1 - The exact dynamical Chern-Simons metric for a spinning black hole possesses a fourth constant of motion

T2 - A dynamical-systems-based conjecture

AU - Cárdenas-Avendaño, Alejandro

AU - Gutierrez, Andrés F.

AU - Pachón, Leonardo A.

AU - Yunes, Nicolás

N1 - Funding Information:
AC-A acknowledges funding from the Fundacion Universitaria Konrad Lorenz (Project 5INV1). NY and AC-A acknowledge financial support through NSF CAREER grant PHY-1250636 and NASA grants NNX16AB98G and 80NSSC17M0041.
Funding Information:
We thank Neil Cornish, Dimitry Ayzenberg, Kent Yagi, Georgios Loukes-Gerakopoulos, Paolo Pani, Andrea Masselli, Charles Kankelborg, Thomas Sotiriou, Olivier Sarbach and Houri Tsuyoshi for very useful suggestions and comments. AC-A acknowledges funding from the Fundación Universitaria Konrad Lorenz (Project 5INV1). NY and AC-A acknowledge financial support through NSF CAREER grant PHY-1250636 and NASA grants NNX16AB98G and 80NSSC17M0041. Computational efforts were performed on the Hyalite High-Performance Computing System, operated and supported by Montana State University’s Information Technology Center.
Publisher Copyright:
© 2018 IOP Publishing Ltd.

PY - 2018/7/20

Y1 - 2018/7/20

N2 - The recent gravitational wave observations by the LIGO/Virgo collaboration have allowed the first tests of general relativity in the extreme gravity regime, when comparable-mass black holes and neutron stars collide. Future space-based detectors, such as the Laser Interferometer Space Antenna, will allow tests of Einstein's theory with gravitational waves emitted when a small black hole falls into a supermassive one in an extreme mass-ratio inspiral. One particular test that is tailor-made for such inspirals is the search for chaos in extreme gravity. We here study whether chaos is present in the motion of test particles around spinning black holes of parity-violating modified gravity, focusing in particular on dynamical Chern-Simons gravity. We develop a resummation strategy that restores all spin terms in the general relativity limit, while retaining up to fifth-order-in-spin terms in the dynamical Chern-Simons corrections to the Kerr metric. We then calculate Poincaré surfaces of section and rotation numbers of a wide family of geodesics of this resummed metric. We find evidence for geodesic chaos, portrayed by thin chaotic layers surrounded by deformed invariant tori. This chaotic layers shrink in size as terms of higher-order in spin are included in the dynamical Chern-Simons corrections to the Kerr metric. Our numerical findings suggest that the geodesics of the as-of-yet unknown exact solution for spinning black holes in this theory may be integrable, and that there may thus exist a fourth integral of motion associated with this exact solution. The studies presented here begin to lay the foundations for chaotic tests of general relativity with the observation of extreme mass ratio inspirals with the Laser Interferometer Space Antenna.

AB - The recent gravitational wave observations by the LIGO/Virgo collaboration have allowed the first tests of general relativity in the extreme gravity regime, when comparable-mass black holes and neutron stars collide. Future space-based detectors, such as the Laser Interferometer Space Antenna, will allow tests of Einstein's theory with gravitational waves emitted when a small black hole falls into a supermassive one in an extreme mass-ratio inspiral. One particular test that is tailor-made for such inspirals is the search for chaos in extreme gravity. We here study whether chaos is present in the motion of test particles around spinning black holes of parity-violating modified gravity, focusing in particular on dynamical Chern-Simons gravity. We develop a resummation strategy that restores all spin terms in the general relativity limit, while retaining up to fifth-order-in-spin terms in the dynamical Chern-Simons corrections to the Kerr metric. We then calculate Poincaré surfaces of section and rotation numbers of a wide family of geodesics of this resummed metric. We find evidence for geodesic chaos, portrayed by thin chaotic layers surrounded by deformed invariant tori. This chaotic layers shrink in size as terms of higher-order in spin are included in the dynamical Chern-Simons corrections to the Kerr metric. Our numerical findings suggest that the geodesics of the as-of-yet unknown exact solution for spinning black holes in this theory may be integrable, and that there may thus exist a fourth integral of motion associated with this exact solution. The studies presented here begin to lay the foundations for chaotic tests of general relativity with the observation of extreme mass ratio inspirals with the Laser Interferometer Space Antenna.

KW - black holes

KW - chaos

KW - general relativity

KW - modified theories of gravity

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U2 - 10.1088/1361-6382/aad06f

DO - 10.1088/1361-6382/aad06f

M3 - Article

AN - SCOPUS:85050718914

SN - 0264-9381

VL - 35

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 16

M1 - 165010

ER -