Horizon thermodynamics in theory *

Abstract

Abstract We investigate whether the new horizon first law still holds in theory. For this complicated theory, we first determine the entropy of a black hole by using the Wald method, and then derive the energy of the black hole by using the new horizon first law, the degenerate Legendre transformation, and the gravitational field equations. For application, we consider the quadratic-curvature gravity, and first calculate the entropy and energy of a static spherically symmetric black hole, which are in agreement with the results obtained in the literature for a Schwarzschild-(A)dS black hole.