Entropy and Energy of Static Spherically Symmetric Black Hole in f(R) Theory

Abstract

We consider the new horizon first law in f (R) theory with general spherically symmetric black hole. We derive the general formulas to computed the entropy and energy of the black hole, which are consistent with the results obtained in the literatures. For applications, some nontrivial black hole solutions in some popular f (R) theories are investigated, the entropies and the energies of black holes in these models are first calculated.

Horizon Thermodynamics in D-Dimensional f(R) Black Hole

“…where W(r) and N(r) are general functions of the coordinate r and the event horizon is local at the largest positive root of N(r + ) = 0 with N (r + ) = 0, the entropy in this case is given by [19]…”

“…Inserting Equations (22) and (19) into Equation 5, then we obtain the energy of black hole (9) in D-dimensional f (R) theory as…”

“…This procedure was firstly investigated for Einstein gravity and Lovelock gravity which only give rise to second-order field equation [ 16 ] and was also applied to gravity with a general static spherically-symmetric black hole in gravity where and are general functions of the coordinate r and the event horizon is local at the largest positive root of with , the entropy in this case is given by [ 19 ] where . The energy is found to be [ 19 ] …”

“…To avoid these two problems, a new horizon-first law was proposed in [ 16 ], where the temperature T and the pressure P are independent thermodynamic quantities and the entropy and free energy are derived concepts, while the horizon-first law can be restored by the Legendre projection. This procedure was generalized to in theory [ 17 ] and theory with a spherically-symmetric black hole [ 18 ] or with a general spherically-symmetric black hole [ 19 ].…”

The Schwarzschild black hole in f(R) can exist superradiation phenomenon

“…The numerical results given in the interesting work show that for the given value of the non dimensional rotation mass ratio of black hole space-time to a/m [10]the non trivial coupling Einstein scalar system has critical memory online α = α(µ); It marks the boundary space-time between the non least coupled large mass scalar field configuration of a multi hairy Kerr black hole and a bald (scalar free) Kerr black hole (where µis the appropriate mass of the non least coupled scalar field). In particular, the critical memory line of the composite system corresponds to the space regularized linearized field configuration black hole supported by the central Kerr (the term "scalar cloud" is usually used in the physical literature [11,12,16,17] to describe these linearized scalar field configurations on the critical existence line of the system).…”