Corrected form of the first law of thermodynamics for regular black holes

Abstract

We show by explicit computations that there is a superficial inconsistency\nbetween the conventional first law of black hole thermodynamics and\nBekenstein-Hawking area law for three types of regular black holes. The\ncorrected form of the first law for these regular black holes is given. The\nderivation relies on the general structure of the energy-momentum tensor of the\nmatter fields. When the black hole mass parameter $M$ is included in the\nenergy-momentum tensor, the conventional form of the first law should be\nmodified with an extra factor. In this case, the black hole mass $M$ can no\nlonger be considered as the internal energy of the regular black holes.\n