Holographic Rényi entropies from hyperbolic black holes with scalar hair

Abstract

The Rényi entropies as a generalization of the entanglement entropy imply much more information. We analytically calculate the Rényi entropies (with a spherical entangling surface) by means of a class of neutral hyperbolic black holes with scalar hair as a one-parameter generalization of the MTZ black hole. The zeroth-order and third-order phase transitions of black holes lead to discontinuity of the Rényi entropies and their second derivatives, respectively. From the Rényi entropies that are analytic at n = ∞, we can express the entanglement spectrum as an infinite sum in terms of the Bell polynomials. We show that the analytic treatment is in agreement with numerical calculations for the low-lying entanglement spectrum in a wide range of parameters.

Finding the Hawking temperature of two new types of topological black holes using the RVB method

“…Although the shape of the black hole is mainly considered to have a spherical topology, supported by the topological theorem for Einstein gravity, recent studies have shown the existence of black objects beyond the spherical horizon in higher dimensional supergravity or string theory. [4][5][6][7][8][9] One such object is the topological black hole, whose metric describing the horizon shape is not a sphere but an Einstein manifold. Topological black holes with planar or hyperbolic horizons have been extensively studied.…”