Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles

Abstract

In several approaches to the quantum-gravity problem evidence has emerged of the validity of a ‘GUP’ (a generalized position–momentum uncertainty principle) and/or a ‘MDR’ (a modification of the energy–momentum dispersion relation), but very little is known about the implications of GUPs and MDRs for black-hole thermodynamics, another key topic for quantum-gravity research. We investigate an apparent link, already suggested in an earlier exploratory study involving two of us, between the possibility of a GUP and/or an MDR and the possibility of a log term in the area–entropy black-hole formula. We then obtain, from that same perspective, a modified relation between the mass of a black hole and its temperature, and we examine the validity of the ‘generalized second law of black-hole thermodynamics’ in theories with a GUP and/or an MDR. After an analysis of GUP- and MDR-modifications of the black-body radiation spectrum, we conclude the study with a description of the black-hole evaporation process.