We study the ultraviolet divergent structures of the matter (scalar) field in a higher $D$-dimensional Reissner-Nordström black hole and compute 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, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon.

• Received 29 July 1996

DOI:https://doi.org/10.1103/PhysRevD.55.2159