https://doi.org/10.1140/epjc/s10052-020-8045-0
Regular Article - Theoretical Physics
Central charges from thermodynamics method in 3D gravity
1
Department of Physics, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran
2
Faculty of Physics, Shahid Bahonar University of Kerman, P.O. Box 76175, Kerman, Iran
* e-mail: d.mahdavian@hsu.ac.ir
Received:
3
April
2020
Accepted:
8
May
2020
Published online:
26
May
2020
In the context of guage/gravity duality, we investigate the central charges of a number of 2-dimensional conformal field theories (CFTs) that might live on the boundary of some 3-dimensional (3D) toy models of gravity, from the thermodynamics aspect of the black holes. For many black hole solutions, the entropy product of the inner Cauchy and outer event horizons is universal (mass independent). It is proposed that for these solutions, the central charges of the left- and right-moving sectors of the dual CFTs should be the same and one may read the central charges from the universal entropy product. This provides strong motivations for investigating this prescription for BTZ and Warped 
black holes in a number of 3D gravity theories and we will show that the proposal works truly. One striking result of our analysis is that if the entropy product is not universal in any theory of 3D gravity, then the left and right central charges are not equal.
© The Author(s), 2020
