Deformations of GR and BH thermodynamics

In four space-time dimensions General Relativity can be non-trivially deformed. Deformed theories continue to describe two propagating degrees of freedom, as GR. We study Euclidean black hole thermodynamics in these deformations. We use the recently developed formulation that works with SO(3) connections as well as certain matrices M of auxiliary fields. We show that the black hole entropy is given by one quarter of the horizon area as measured by the Lie algebra valued two-form MF, where F is the connection curvature. This coincides with the horizon area as measured by the metric only for the case of General Relativity.