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Lessons from black hole quasinormal modes in modified gravity

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Abstract

Quasinormal modes (QNMs) of perturbed black holes have recently gained much interest because of their tight relations with the gravitational wave signals emitted during the post-merger phase of a binary black hole coalescence. One of the intriguing features of these modes is that they respect the no-hair theorem, and hence, they can be used to test black hole spacetimes and the underlying gravitational theory. In this paper, we exhibit three different aspects of how black hole QNMs could be altered in theories beyond Einstein’s general relativity (GR). These aspects are (i) the direct alterations of QNM spectra as compared with those in GR, (ii) the violation of the geometric correspondence between the high-frequency QNMs and the photon geodesics around the black hole, and (iii) the breaking of the isospectrality between the axial and polar gravitational perturbations. Several examples will be provided in each individual case. The prospects and possible challenges associated with future observations will be also discussed.

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Notes

  1. Extending gravitational theories of gravity beyond GR has been motivated by both theoretical and astrophysical reasons. These include the resolution of spacetime singularities, incorporating quantum effects in gravity, and the mysterious dark sectors in the universe. For reviews in modified theories of gravity, we refer the readers to Refs. [4, 5].

  2. We do not consider the perturbations of black holes which are asymptotically anti-de Sitter here. In these cases, one has to adopt different boundary conditions and the WKB method is not applicable anymore [23].

  3. We will rescale all the quantities with respect to the black hole mass by setting \(M=1/2\).

  4. The real part of the eikonal QNM frequencies can be further related to the apparent size of the black hole shadow, which is directly related to the spherical photon orbits [59,60,61].

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Acknowledgements

CYC is supported by Institute of Physics of Academia Sinica. The work of MBL is supported by the Basque Foundation of Science Ikerbasque. She also would like to acknowledge the partial support from the Basque government Grant No. IT956-16 (Spain) and from the project FIS2017-85076-P (MINECO/AEI/FEDER, UE). PC is supported by Ministry of Science and Technology (MOST), Taiwan, through no. 107-2119-M-002-005, Leung Center for Cosmology and Particle Astrophysics (LeCosPA) of National Taiwan University, and Taiwan National Center for Theoretical Sciences (NCTS).

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Chen, CY., Bouhmadi-López, M. & Chen, P. Lessons from black hole quasinormal modes in modified gravity. Eur. Phys. J. Plus 136, 253 (2021). https://doi.org/10.1140/epjp/s13360-021-01227-z

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