Horizon Thermodynamics In F(R) Theory

This paper investigates whether the new horizon first law still work in f(R)theory.In general relativity,the entropy and energy of a static spherically symmetric black hole can be obtained from the new horizon first law.In the case of f(R)gravitation,the gravitational field equation is obtained by taking into account the minimum coupling of matter and the variation of the action.In the case of static spherically symmetric spacetime,assuming the form of the equation of state at the event horizon,the radial field equation of f(R)gravity is written as a combination of two parts,one of which contains the temperature term and the other does not.At the event horizon,assuming a small change in the radius of the horizon,the differential form of the new horizon first law can be obtained,and then the integral formula for calculating the entropy and energy of the black hole can be obtained.As applications,the solutions of some nontrivial black holes in f(R)gravitation,such as the constant Ricci curvature black holes and the non-constant Ricci curvature black holes,are studied.According to the nonnegative entropy and energy,new limits of the parameters of f(R)gravity are given.