Black Hole Remnants from Dynamical Dimensional Reduction?

Abstract

A intriguing feature shared by many quantum gravity programs is the dynamical decrease of the spectral dimension from $D_s = 4$ at macroscopic to $D_s \approx 2$ at microscopic scales. In this note, we study the impact of this transition on the energy loss of static, spherically symmetric black holes due to Hawking radiation. We demonstrate that the decrease in the spectral dimension renders the luminosity of a black hole finite. While this slightly increases the life-time of light black holes, we find that this mechanism is insufficient to generate long-lived black hole remnants. We briefly comment on the relation of our findings to previous work on this topic.