Ten shades of black

Abstract

The holographic principle has taught us that, as far as their entropy content is concerned, black holes in $(3+1)$-dimensional curved spacetimes behave as ordinary thermodynamic systems in flat $(2+1)$-dimensional spacetimes. In this essay we point out that the opposite behavior can also be observed in black-hole physics. To show this we study the quantum Hawking evaporation of near-extremal Reissner-Nordstr\"om black holes. We first point out that the black-hole radiation spectrum departs from the familiar radiation spectrum of genuine $(3+1)$-dimensional perfect black-body emitters. In particular, the would be black-body thermal spectrum is distorted by the curvature potential which surrounds the black hole and effectively blocks the emission of low-energy quanta. Taking into account the energy-dependent gray-body factors which quantify the imprint of passage of the emitted radiation quanta through the black-hole curvature potential, we reveal that the $(3+1)$-dimensional black holes effectively behave as perfect black-body emitters in a flat $(9+1)$-dimensional spacetime.