2000 character limit reached
Quadratic Quasi-Normal Modes of a Schwarzschild Black Hole (2405.06012v2)
Published 9 May 2024 in gr-qc, astro-ph.CO, astro-ph.HE, and hep-th
Abstract: Quadratic quasi-normal modes, generated at second order in black hole perturbation theory, are a promising target for testing gravity in the nonlinear regime with next-generation gravitational wave detectors. While their frequencies have long been known, their amplitudes remain poorly studied. We introduce regular variables and compute amplitudes for Schwarzschild black holes with the Leaver algorithm. We find a nonlinear ratio $\mathcal{R}\simeq0.154e{-0.068i}$ for the most excited $\ell=4$ mode, matching results from Numerical Relativity. We also predict new low-frequency $\ell=2$ quadratic modes.
- E. Berti, V. Cardoso, and A. O. Starinets, Quasinormal modes of black holes and black branes, Classical and Quantum Gravity 26, 163001 (2009).
- E. Berti, V. Cardoso, and C. M. Will, Gravitational-wave spectroscopy of massive black holes with the space interferometer lisa, Physical Review D 73, 10.1103/physrevd.73.064030 (2006).
- R. Brito, A. Buonanno, and V. Raymond, Black-hole Spectroscopy by Making Full Use of Gravitational-Wave Modeling, Phys. Rev. D 98, 084038 (2018), arXiv:1805.00293 [gr-qc] .
- V. Baibhav and E. Berti, Multimode black hole spectroscopy, Phys. Rev. D 99, 024005 (2019), arXiv:1809.03500 [gr-qc] .
- C. D. Capano and A. H. Nitz, Binary black hole spectroscopy: a no-hair test of GW190814 and GW190412, Phys. Rev. D 102, 124070 (2020), arXiv:2008.02248 [gr-qc] .
- I. Ota and C. Chirenti, Black hole spectroscopy horizons for current and future gravitational wave detectors, (2021), arXiv:2108.01774 [gr-qc] .
- N. Franchini and S. H. Völkel, Parametrized quasinormal mode framework for non-Schwarzschild metrics, Phys. Rev. D 107, 124063 (2023), arXiv:2210.14020 [gr-qc] .
- A. Ghosh, R. Brito, and A. Buonanno, Constraints on quasinormal-mode frequencies with LIGO-Virgo binary–black-hole observations, Phys. Rev. D 103, 124041 (2021), arXiv:2104.01906 [gr-qc] .
- R. Abbott et al. (LIGO Scientific, Virgo), Tests of general relativity with binary black holes from the second LIGO-Virgo gravitational-wave transient catalog, Phys. Rev. D 103, 122002 (2021), arXiv:2010.14529 [gr-qc] .
- T. Regge and J. A. Wheeler, Stability of a Schwarzschild singularity, Phys.Rev. 108, 1063 (1957).
- F. J. Zerilli, Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics, Physical Review D 2, 2141 (1970).
- L. London, D. Shoemaker, and J. Healy, Modeling ringdown: Beyond the fundamental quasinormal modes, Physical Review D 90, 10.1103/physrevd.90.124032 (2014).
- K. Mitman et al., Nonlinearities in Black Hole Ringdowns, Phys. Rev. Lett. 130, 081402 (2023), arXiv:2208.07380 [gr-qc] .
- M. H.-Y. Cheung et al., Nonlinear Effects in Black Hole Ringdown, Phys. Rev. Lett. 130, 081401 (2023), arXiv:2208.07374 [gr-qc] .
- H. Zhu et al., Nonlinear Effects In Black Hole Ringdown From Scattering Experiments I: spin and initial data dependence of quadratic mode coupling, (2024), arXiv:2401.00805 [gr-qc] .
- M. Lagos and L. Hui, Generation and propagation of nonlinear quasinormal modes of a schwarzschild black hole, Physical Review D 107, 10.1103/physrevd.107.044040 (2023).
- H. Nakano and K. Ioka, Second Order Quasi-Normal Mode of the Schwarzschild Black Hole, Phys. Rev. D 76, 084007 (2007), arXiv:0708.0450 [gr-qc] .
- K. Ioka and H. Nakano, Second and higher-order quasi-normal modes in binary black hole mergers, Phys. Rev. D 76, 061503 (2007), arXiv:0704.3467 [astro-ph] .
- S. Ma and H. Yang, The excitation of quadratic quasinormal modes for Kerr black holes, (2024), arXiv:2401.15516 [gr-qc] .
- D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Second and higher-order perturbations of a spherical spacetime, Phys. Rev. D 74, 044039 (2006), arXiv:gr-qc/0607025 .
- D. Brizuela, J. M. Martin-Garcia, and G. A. M. Marugan, High-order gauge-invariant perturbations of a spherical spacetime, Phys. Rev. D 76, 024004 (2007), arXiv:gr-qc/0703069 .
- D. Brizuela, J. M. Martin-Garcia, and M. Tiglio, A Complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole, Phys. Rev. D 80, 024021 (2009), arXiv:0903.1134 [gr-qc] .
- E. W. Leaver, An analytic representation for the quasi-normal modes of kerr black holes, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 402, 285 (1985).
- https://github.com/akuntz00/QuadraticQNM.
- R. Sachs, Gravitational Waves in General Relativity. VI. The Outgoing Radiation Condition, Proceedings of the Royal Society of London Series A 264, 309 (1961).
- R. K. Sachs, Gravitational Waves in General Relativity. VIII. Waves in Asymptotically Flat Space-Time, Proceedings of the Royal Society of London Series A 270, 103 (1962).
- E. Newman and R. Penrose, An Approach to Gravitational Radiation by a Method of Spin Coefficients, Journal of Mathematical Physics 3, 566 (1962).
- M. Isi and W. M. Farr, Analyzing black-hole ringdowns, (2021), arXiv:2107.05609 [gr-qc] .
- R. Abbott et al. (LIGO Scientific, Virgo), GW190521: A Binary Black Hole Merger with a Total Mass of 150M⊙150subscript𝑀direct-product150M_{\odot}150 italic_M start_POSTSUBSCRIPT ⊙ end_POSTSUBSCRIPT, Phys. Rev. Lett. 125, 101102 (2020), arXiv:2009.01075 [gr-qc] .
- Black Hole Perturbation Toolkit, (bhptoolkit.org).
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.