INCREASE OF BLACK-HOLE ENTROPY IN HIGHER CURVATURE GRAVITY

We examine the zeroth law and the second law of black hole thermodynam ics within the context of effective gravitational actions including hi gher curvature interactions. We show that entropy can never decrease f or quasistationary processes in which a black hole accretes positive e nergy matter, independent of the details of the gravitational action. Within a class of higher curvature theories where the Lagrangian consi sts of a polynomial in the Ricci scalar, we use a conformally equivale nt theory to establish that stationary black hole solutions with a Kil ling horizon satisfy the zeroth law, and that the second law holds in general for any dynamical process. We also introduce a new method for establishing the second law based on a generalization of the area theo rem, which may prove useful for a wider class of Lagrangians. Finally, we show how one can infer the form of the black hole entropy, at leas t for the Ricci polynomial theories, by integrating the changes of mas s and angular momentum in a quasistationary accretion process.