Black hole thermodynamics

Black holes are singular solutions of Einstein's equations. It turns out that they also satisfy thermodynamic laws if we identify some of their geometric properties with thermodynamic property. This thermodynamic nature indicates that black holes are probably a macroscopic manifestation of a collection of large number of microstates. Now it is possible to correct Einstein's equation with what we generically call 'higher curvature' terms. A natural question arises that to what extent such new corrections can preserve the thermodynamic nature of the 'corrected' black hole solutions and also why should we at all expect them to preserve (or not to preserve) these properties. To my understanding, these questions have not yet been answered in complete generality. In this talk I shall attempt to describe some parts of this problem.