Black Hole Evaporation and Compact Extra Dimensions

TL;DR

The paper investigates black hole evaporation in spacetimes with large compact extra dimensions of size $L$, focusing on how the evaporation rate depends on the horizon radius $R_H$ relative to $L$ and on the dimensionality $d$. It develops an interpolating description of the $4+d$-dimensional metric and analyzes evaporation under both canonical and microcanonical statistics, showing that luminosity is strongly damped as $R_H$ approaches $L$ and that small BHs ($R_H\ll L$) are quasi-stable due to higher-dimensional effects and angular-momentum barriers. It identifies a first-order phase transition near $R_H\sim L$, accompanied by a horizon topology change from cylindrical to spherical and possibly an energy outburst, leaving quasi-stable remnants at $M\sim M_c$ with $M_c = m_p\,L/\ell_p$. These results have implications for primordial black holes and cosmology, offering potential signatures of large extra dimensions through altered evaporation histories and remnants.

Abstract

We study the evaporation of black holes in space-times with extra dimensions of size L. We first obtain a description which interpolates between the expected behaviors of very large and very small black holes and then show that the luminosity is greatly damped when the horizon shrinks towards L from a larger value. Analogously, black holes born with an initial size smaller than L are almost stable. This effect is due to the dependence of both the Hawking temperature and the grey-body factor of a black hole on the dimensionality of space. Although the picture of what happens when the horizon becomes of size L is still incomplete, we argue that there occurs a (first order) phase transition, possibly signaled by an outburst of energy which leaves a quasi-stable remnant.

Figures (6)

• Figure 1: Plot of the horizon for $d=1$ and $M=M_c$, $0.8\,M_c$, $0.6\,M_c$, $0.4\,M_c$ (in units with $G=L=1$). For $d=0$ the corresponding horizons would be at $r_b=2$, $1.6$, $1.2$, $0.8$.
• Figure 2: Decay rate for a large ($R_H\gg L$) black hole.
• Figure 3: Decay rate for a small black hole in increasing number of extra dimensions ($d=0$ uppermost curve, $d=4$ lowest curve). Vertical units are arbitrary.
• Figure 4: History of a small [$M(0)\sim M_c$] black hole in increasing number of extra dimensions ($d=0$ lowest curve, $d=4$ uppermost curve). Horizontal units are arbitrary.
• Figure 5: Potential $V_1+V_2$ for different numbers of extra dimensions ($d=4$ uppermost curve, $d=0$ lowest curve).