Abstract
We use holography in order to study the entropy of thermal CFTs on (1+1)-dimensional curved backgrounds that contain horizons. Starting from the metric of the BTZ black hole, we perform explicit coordinate transformations that set the boundary metric in de Sitter or black-hole form. For a de Sitter boundary, the dual picture describes a CFT at a temperature different from that of the cosmological 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's constant. We find that the leading contribution to the entropy is proportional to the horizon area, with a coefficient that accounts for the degrees of freedom of a CFT thermalized above the horizon temperature. We demonstrate the universality of our findings by considering the most general metric in a (2+1)-dimensional AdS bulk containing a non-rotating black hole and a static boundary with horizons.
Highlights
The relation between entanglement and gravitational entropy in spaces that contain horizons can shed light on the fundamental nature of gravity
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 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
Summary
The relation between entanglement and gravitational entropy in spaces that contain horizons can shed light on the fundamental nature of gravity. The other is the bulk black hole horizon that specifies the temperature of the dual-field theory. While both of them indicate a thermal behavior, their crucial difference lies in the fact that the cosmological horizon is observer dependent and the effects of curvature cannot be disentangled from thermal effects. The dual theory is in a generalization of the Hartle-Hawking state with the environment at a higher temperature than the boundary black hole Such a configuration is possible because the CFT stress-energy tensor diverges on the black hole horizon. V we generalize our results for an arbitrary static boundary metric with horizons
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