We examine the Zeroth Law and the Second Law of black hole thermodynamics
within the context of effective gravitational actions including higher
curvature interactions. We show that entropy can never decrease for
quasi-stationary processes in which a black hole accretes positive energy
matter, independent of the details of the gravitational action. Within a class
of higher curvature theories where the Lagrangian consists of a polynomial in
the Ricci scalar, we use a conformally equivalent theory to establish that
stationary black hole solutions with a Killing 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 theorem, 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 least for the Ricci polynomial theories, by integrating the changes
of mass and angular momentum in a quasistationary accretion process.Comment: 20 pages, LaTe
