Probability for Primordial Black Holes in Higher Dimensional Universe

TL;DR

This paper explores the likelihood of primordial black hole formation in higher-dimensional universes using semiclassical quantum cosmology, comparing different topologies and their probabilities under specific boundary conditions.

Contribution

It introduces a framework for calculating the probability of black hole pair creation in higher-dimensional cosmological models with Hartle-Hawking boundary conditions.

Findings

Higher dimensional universes with black hole pairs are less probable to nucleate when extra dimensions are static.

The probability depends on the topology of the spatial sections, favoring certain configurations over others.

Black hole pair creation probability is lower in models with non-varying extra dimensions during inflation.

Abstract

We investigate higher dimensional cosmological models in the semiclassical approximation with Hartle-Hawking Boundary conditions, assuming a gravitational action which is described by the scalar curvature with a cosmological constant. In the framework the probability for quantum creation of an inflationary universe with a pair of black holes in a multidimensional universe is evaluated. The probability for creation of a universe with a spatial section with $S^{1}XS^{D -2}$ topology is then compared with that of a higher dimensional de Sitter universe with $S^{D -1}$ spatial topology. It is found that a higher dimensional universe with a product space with primordial black holes pair is less probable to nucleate when the extra dimensions scale factors do not vary in an inflating universe.