https://doi.org/10.1140/epjc/s10052-024-13209-3
Regular Article – Theoretical Physics
Rotating black holes in a viable Lorentz-violating gravity: finding exact solutions without tears
Center for Quantum Spacetime, Sogang University, 121-742, Seoul, South Korea
Received:
23
May
2024
Accepted:
6
August
2024
Published online:
24
August
2024
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 region from the ring singularity at in Boyer–Lindquist coordinates. There are two Killing horizons where 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 under the foliation-preserving diffeomorphism , 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.
Dedicated to the memory of Roman Jackiw (8 November 1939–14 June 2023).
© The Author(s) 2024
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