Geometric model of black hole quantum $N$-portrait, extradimensions and thermodynamics

Abstract

Recently a short scale modified black hole metric, known as holographic metric, has been proposed in order to capture the self-complete character of gravity. In this paper we show that such a metric can reproduce some geometric features expected from the quantum $N$-portrait beyond the semi-classical limit. We show that for a generic $N$ this corresponds to having an effective energy momentum tensor in Einstein equations or, equivalently, non-local terms in the gravity action. We also consider the higher dimensional extension of the metric and the case of an AdS cosmological term. We provide a detailed thermodynamic analysis of both cases, with particular reference to the repercussions on the Hawking-Page phase transition.Comment: 36 pages, 8 figures, invited paper to the special issue "Entropy in Quantum Gravity and Quantum Cosmology" edited by R. Garattini for the journal "Entropy", accepted for publication; v2 version matching that published on the journa