Petrov Type, Principal Null Directions, and Killing Tensors of Slowly-Rotating Black Holes in Quadratic Gravity
arXiv:2103.15891 · doi:10.1103/PhysRevD.103.124057
Abstract
The ability to test general relativity in extreme gravity regimes using gravitational wave observations from current ground-based or future space-based detectors motivates the mathematical study of the symmetries of black holes in modified theories of gravity. In this paper we focus on spinning black hole solutions in two quadratic gravity theories: dynamical Chern-Simons and scalar Gauss-Bonnet gravity. We compute the principal null directions, Weyl scalars, and complex null tetrad in the small-coupling, slow rotation approximation for both theories, confirming that both spacetimes are Petrov type I. Additionally, we solve the Killing equation through rank 6 in dynamical Chern-Simons gravity and rank 2 in scalar Gauss-Bonnet gravity, showing that there is no nontrivial Killing tensor through those ranks for each theory. We therefore conjecture that the still-unknown, exact, quadratic-gravity, black-hole solutions do not possess a fourth constant of motion.
23 pages, 2 figures, reuploaded on 01/04/24 to correct small typo in Eq (C5)
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- Quasinormal modes of slowly-rotating black holes in dynamical Chern-Simons gravity
- Quasi-normal mode frequencies and gravitational perturbations of black holes with any subextremal spin in modified gravity through METRICS: the scalar-Gauss-Bonnet gravity case
- Spectral method for metric perturbations of black holes: Kerr background case in general relativity
- Spectral Method for the Gravitational Perturbations of Black Holes: Schwarzschild Background Case
- Parameterizations of black-hole spacetimes beyond circularity
- Gravitational wave from extreme mass-ratio inspirals as a probe of extra dimensions
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