Rotating black holes in a viable Lorentz-violating gravity: finding exact solutions without tears

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2024-08, Vol.84 (8), p.852-13, Article 852
• Main Authors: Devecioğlu, Deniz O., Park, Mu-In
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Black holes; Cosmological constant; Couplings; Elementary Particles; Exact solutions; Hadrons; Hamilton-Jacobi equation; Heavy Ions; Isomorphism; Light speed; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article – Theoretical Physics; Rotation; String Theory
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-024-13209-3

We introduce a two-step procedure for finding Kerr-type rotating black hole solutions without tears. Considering the low-energy sector of Hořava gravity as a viable Lorentz-violating gravity in four dimensions which admits a different speed of gravity, we find the exact rotating black hole solutions (with or without cosmological constant). We find that the singular region extends to r < 0 region from the ring singularity at r = 0 in Boyer–Lindquist coordinates. There are two Killing horizons where g rr = 0 and the black hole thermodynamics laws are still valid. We find the rotating black hole solutions with electromagnetic charges only when we consider the noble electromagnetic couplings, in such a way that the speed of light is the same as the speed of gravity. With the noble choice of couplings, our Lorentz-violating gravity can be consistent with the recently-observed time delay of the coincident GW and GRB signals. Furthermore, in Appendices, we show that (a) the uniqueness of the invariant line element d s 2 under the foliation-preserving diffeomorphism Diff F , contrary to Lorentz-violating action, (b) the solutions are the Petrov type I with four distinct principal null vectors, and (c) the Hamilton-Jacobi equation for the geodesic particles are not separable.