https://doi.org/10.1140/epjc/s10052-016-3960-9
Regular Article - Theoretical Physics
An exploration of the black hole entropy via the Weyl tensor
1
Department of Physics, College of Sciences, Northeastern University, Shenyang, 110819, China
2
Department of Astronomy, Beijing Normal University, Beijing, 100875, China
3
Department of Physics, Beijing Normal University, Beijing, 100875, China
* e-mail: linan@mail.neu.edu.cn
Received:
2
November
2015
Accepted:
19
February
2016
Published online:
1
March
2016
The role of the Weyl tensor 
in black hole thermodynamics is explored by looking at the relation between the scalar invariant 
and the entropy of n-dimensional static black holes. It is found that this invariant can be identified as the entropy density of the gravitational fields for classical 5-dimensional black holes. We calculate the proper volume integrals of for the Schwarzschild and Schwarzschild–anti-de Sitter black holes and show that these integrals correctly lead to the Bekenstein–Hawking entropy formulas, only up to some coefficients. ’
© The Author(s), 2016
