Evaporation of Microscopic Black Holes in String Theory and the Bound on Species

TL;DR

This paper investigates how string theory compactifications with D-branes comply with the black hole species bound, revealing that the effective number of string states black holes can evaporate into is limited, preserving semi-classical black hole existence.

Contribution

It demonstrates that the exponential growth of string states does not violate the black hole bound, establishing a bound N = 1/g_s^2 on the effective species number in string compactifications.

Findings

Black hole bound is saturated by Kaluza-Klein particles.

The effective number of string resonances is bounded by N = 1/g_s^2.

Semi-classical black holes of sub-stringy size can exist despite many string states.

Abstract

We address the question how string compactifications with D-branes are consistent with the black hole bound, which arises in any theory with number of particle species to which the black holes can evaporate. For the Kaluza-Klein particles, both longitudinal and transversal to the D-branes, it is relatively easy to see that the black hole bound is saturated, and the geometric relations can be understood in the language of species-counting. We next address the question of the black hole evaporation into the higher string states and discover, that contrary to the naive intuition, the exponentially growing number of Regge states does not preclude the existence of semi-classical black holes of sub-stringy size. Our analysis indicates that the effective number of string resonances to which such micro black holes evaporate is not exponentially large but is bounded by N = 1/g_s^2, which suggests the interpretation of the well-known relation between the Planck and string scales as the saturation of the black hole bound on the species number. In addition, we also discuss some other issues in D-brane compactifications with a low string scale of order TeV, such as the masses of light moduli fields.