Quantum Gravitational Corrections to the Geometry of Charged AdS Black Holes

Abstract

We study the quantum gravitational corrections to the geometry of a four-dimensional charged (Reissner-Nordström) Anti de Sitter black hole starting from an effective field theory approach to quantum gravity. We use the expression of the modified horizon radius to compute the quantum corrected Wald entropy, whose expression reproduces the logarithmic behaviour found by other methods. We perform a thermodynamics analysis and compute the quantum gravitational corrections to the temperature, pressure, specific heat and Helmholtz free energy. All these quantities are renormalisation group invariant. We find that a quantum charged AdS black hole can exist only for a bounded range of masses and that it can undergo a second order phase transition as it moves from a state with positive specific heat to a negative one.

Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy

“…As a matter of fact, this should be seen as some "quantum" backreaction in the geometry due to Gaussian fluctuations in the thermal partition function [89]. The backreaction can be modeled by adding the Barvinsky-Vilkovisky-de Witt non-local effective action [90][91][92] that, indeed, produces the logarithmic corrections on the black hole entropy [66,[93][94][95]. The deformations can break the original black hole symmetries generating terms of the form of (5.1), as can be seen in [95].…”

“…The backreaction can be modeled by adding the Barvinsky-Vilkovisky-de Witt non-local effective action [90][91][92] that, indeed, produces the logarithmic corrections on the black hole entropy [66,[93][94][95]. The deformations can break the original black hole symmetries generating terms of the form of (5.1), as can be seen in [95]. This could lead to model breaking of conformal invariance in the AdS boundary when the quantum corrections dominate over the saddle, as could be for final stages of black hole due to evaporation.…”

Logarithmic correction to black hole entropy in universal low-energy string theory models

“…In the large-charge limit 2 of black holes, the logarithmic correction is fully dominant over others. These logarithmic entropy corrections also turn out to be universal since they are inescapable in the structure of every quantum gravity, even via many different approaches like -Euclidean effective action method [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], quantum tunneling [21][22][23], conical singularity [17,18], Cardy formula [20], conformal anomaly [24], quantum geometry [19], non-local quantum gravity [44][45][46][47], etc. For a gravity model coupled to the higher-curvature terms beyond two-derivative, the expansion (1.1) in principle holds a similar form, except the BHAL gets modified into the Bekenstein-Hawking-Wald formula [50] by capturing the classical higher-derivative corrections to black hole entropy.…”