Rotating BTZ-like black hole and central charges in Einstein-bumblebee gravity

Chikun Ding; Yu Shi; Jun Chen; Yuebing Zhou; Changqing Liu; Yuehua Xiao

doi:10.1140/epjc/s10052-023-11761-y

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 573
https://doi.org/10.1140/epjc/s10052-023-11761-y

Regular Article - Theoretical Physics

Rotating BTZ-like black hole and central charges in Einstein-bumblebee gravity

Chikun Ding¹^,2^a, Yu Shi¹, Jun Chen¹, Yuebing Zhou¹, Changqing Liu¹ and Yuehua Xiao¹

¹ Department of Physics, Huaihua University, 418008, Huaihua, People’s Republic of China
² Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, 410081, Changsha, Hunan, People’s Republic of China

^a dingchikun@163.com, dck@hhtc.edu.cn

Received: 15 May 2023
Accepted: 25 June 2023
Published online: 6 July 2023

Abstract

We obtain an exact rotating BTZ-like black hole solution by solving the corresponding gravitational field equations and the bumblebee motion equations in Einstein-bumblebee gravity theory. Result is presented for the purely radial Lorentz symmetry violating and can only exist with a linear functional potential of the bumblebee field. This black hole has two horizons and an ergosphere which are dependent on the bumblebee coupling constant $ℓ$ $\ell$ . The concepts of the area and volume of the horizon should be renewed in this LV spacetime due to the nontrivial contribution of coupling between the bumblebee field and the Ricci tensor. Only in this way, the entropy-area relation, first law of thermodynamics and the Smarr formula can still be constructed. We also study the AdS/CFT correspondence of this black hole, find that the entropy product of its inner and outer horizons is universal. So the central charges of the dual CFT on the boundary can be obtained via the thermodynamic method, and they can reappear black hole mass and angular momentum in the bulk.

© The Author(s) 2023

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