Black Holes and Sub-millimeter Dimensions

TL;DR

The paper investigates black holes in a brane-world scenario with large extra dimensions and TeV-scale gravity, focusing on small black holes whose radii are below the compactification scale. It derives (4+n)-dimensional scaling laws for horizon radius, temperature, and lifetime, revealing that such black holes are larger, colder, and longer-lived than their 4D counterparts and primarily radiate into bulk gravitons. This leads to a dramatic suppression of observable Standard Model signatures from Hawking evaporation, weakening traditional PBH bounds from gamma rays and BBN while enhancing PBH production under the brane-world geometry. Consequently, the primordial spectral index bounds are relaxed (N ≲ 1.47–1.59 depending on n), and PBHs can serve as dark matter candidates or seeds for early structure for certain numbers of extra dimensions.

Abstract

Recently, a new framework for solving the hierarchy problem was proposed which does not rely on low energy supersymmetry or technicolor. The fundamental Planck mass is at a TeV and the observed weakness of gravity at long distances is due the existence of new sub-millimeter spatial dimensions. In this letter, we study how the properties of black holes are altered in these theories. Small black holes---with Schwarzschild radii smaller than the size of the new spatial dimensions---are quite different. They are bigger, colder, and longer-lived than a usual $(3+1)$-dimensional black hole of the same mass. Furthermore, they primarily decay into harmless bulk graviton modes rather than standard-model degrees of freedom. We discuss the interplay of our scenario with the holographic principle. Our results also have implications for the bounds on the spectrum of primordial black holes (PBHs) derived from the photo-dissociation of primordial nucleosynthesis products, distortion of the diffuse gamma-ray spectrum, overclosure of the universe, gravitational lensing, as well as the phenomenology of black hole production. For example, the bound on the spectral index of the primordial spectrum of density perturbations is relaxed from 1.25 to 1.45-1.60 depending on the epoch of the PBH formation. In these scenarios PBHs provide interesting dark matter candidates; for 6 extra dimensions MACHO candidates with mass $\sim 0.1M_\odot$ can arise. For 2 or 3 extra dimensions PBHs with mass $\sim 2000 M_\odot$ can occur and may act as both dark matter and seeds for early galaxy and QSO formation.