Entropy of thermal CFTs on curved backgrounds

We use holography in order to study the entropy of thermal conformal field theory (CFT) on (1 þ 1)- dimensional curved backgrounds that contain horizons. Starting from the metric of the BañadosTeitelboim-Zanelli (BTZ) black hole, we perform explicit coordinate transformations that set the boundary metric in de Sitter or black hole form. The dual picture describes a CFT at a temperature different from that of the horizon. We determine minimal surfaces that allow us to compute the entanglement entropy of a boundary region, as well as the temperature affecting the energy associated with a probe quark on the boundary. For an entangling surface that coincides with the horizon, we study the relation between entanglement and gravitational entropy through an appropriate definition of the effective Newton constant. We find that the leading contribution to the entropy is proportional to the horizon area, with a coefficient that exceeds the standard value for the Bekenstein-Hawking entropy. The difference is attributed to the divergence of the stress-energy tensor of the thermal CFT on the horizon. We demonstrate the universality of these findings by considering the most general metric in a (2 þ 1)-dimensional anti–de Sitter bulk containing a nonrotating black hole and a static boundary with horizons