RENORMALIZED THERMODYNAMIC ENTROPY OF BLACK-HOLES IN HIGHER DIMENSIONS

We study the ultraviolet divergent structures of the matter (scalar) f ield in a higher D-dimensional Reissner-Nordstrom black hole and compu te the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yi eld the correct renormalization of the gravitational coupling constant s. In particular, we show that the matter field contribution in odd di mensions does not give the term proportional to the area of the black hole event horizon.