Black Hole Thermodynamics In High-order Gravitational Theory

This paper investigated whether the new horizon first law still holds in high-order gravitational theory,such as f(R,R_?vR^?v) gravity.The entropy and energy of a static spherically symmetric black hole can be directly derived from the field equations of the general relativity and the first law of the new horizon.Using this method and the f(R) gravity theory found that the same results can be obtained.Then we considered the f(R,R_?vR^?v) gravitational theory.we first determine the equation field by the variation of the action Secondly,the entropy and energy are calculated by 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 Schwarzschild-(A)DS black hole,which are in agreement with the results obtained in the literature.