Violation of the first law of black hole thermodynamics in f(T) gravity

Abstract

We prove that, in general, the first law of black holethermodynamics, δQ = TδS, is violated in f(T) gravity.As a result, it is possible that there exists entropy production,which implies that the black hole thermodynamics can be innon-equilibrium even in the static spacetime. This feature is verydifferent from that of f(R) or that of other higher derivativegravity theories. We find that the violation of first law resultsfrom the lack of local Lorentz invariance in f(T) gravity. Byinvestigating two examples, we note that f′′(0) should be negativein order to avoid the naked singularities and superluminal motion oflight. When f′′(T) is small, the entropy of black holes in f(T)gravity is approximatively equal to f′(T)/4 A.