Near horizon symmetry and entropy of black holes in the presence of a conformally coupled scalar

Abstract

We analyze the near horizon conformal symmetry for black hole solutions in gravity with a conformally coupled scalar field using the method proposed by Majhi and Padmanabhan recently. It is shown that the entropy of the black holes of the form $\mathrm{d}s^2 = - f(r)\mathrm{d}t^2 + \mathrm{d}r^2/f(r)+...$ agrees with Wald entropy. This result is different from previous result obtained by M. Natsuume, T. Okamura and M. Sato using the canonical Hamiltonian formalism, which claims a discrepancy from Wald entropy.