CHARGED BLACK-HOLES IN QUADRATIC THEORIES

We point out that in general the Reissner-Nordstrom (RN) charged black holes of general relactivity are not solutions of the four-dimensional quadratic gravitational theories. They are, e.g., exact solutions of the R + R2 quadratic theory but not of a theory where a R(ab)R(ab) term is present in the gravitational Lagrangian. In the case where such a nonlinear curvature term is present with sufficiently small coupling we obtain an approximate solution for a charged black hole of charge Q and mass M. For Q much less than M the validity of this solution extends down to the horizon. This allows us to explore the thermodynamic properties of the quadratic charged black hole and we find that, to our approximation, its thermodynamics is identical to that of a RN black hole. However our black hole's entropy is not equal to one-fourth of the horizon area. Finally we extend our analysis to the rotating charged black hole and qualitatively similar results are obtained.