Generalized black hole entropy in two dimensions
Abstract
The Bekenstein–Hawking entropy of a black hole is proportional to its horizon area, hence in D=2 spacetime dimensions it is constant because the horizon degenerates into two points. This fact is consistent with Einstein’s gravity becoming topological in two dimensions. In F(R) gravity, which is non-trivial even in D=2, we find that the entropy is constant, as for Bekenstein–Hawking. As shown in Europhys. Lett. 139(6) (2022) 69001, arXiv: 2208.10146, two-dimensional F(R) gravity is equivalent to Jackiw–Teitelboim gravity, in turn, equivalent to the Sachdev–Ye–Kitaev model where the entropy becomes constant in the large N limit. Several recently proposed entropies are functions of the Bekenstein–Hawking entropy and become constant in D=2, but in two-dimensional dilaton gravity entropies are not always constant. We study general dilaton gravity and obtain arbitrary static black hole solutions for which the non-constant entropies depend on the mass, horizon radius, or Hawking temperature, and constitute new proposals for a generalized entropy.
