PERTURBATIVE METRIC OF CHARGED BLACK-HOLES IN QUADRATIC GRAVITY

We consider perturbative solutions to the classical field equations coming from a quadratic gravitational Lagrangian in four dimensions. We study the charged, spherically symmetric black hole, and explicitly give corrections up to third order (in the coupling constant multiplying the R R term) to the Reissner-Nordström metric. We discuss the thermodynamics of such black holes; in particular, we compute explicitly its temperature and entropy-area relation. The latter deviates from the usual S=A/4 expression, depending also on the charge Q, and on nonlinearly. © 1995 The American Physical Society.