Extra Dimensions and Possible Space-Time Signature Changes

TL;DR

This paper explores higher-dimensional Einstein-Maxwell-scalar solutions with internal spaces, identifying conditions for horizons, including black holes and space-time signature-changing horizons, and analyzes their stability, finding black holes are stable while others are not.

Contribution

It provides new exact solutions with scalar and electromagnetic fields in higher dimensions, characterizes horizon types, and proves stability properties of these solutions.

Findings

Black-hole solutions are stable under perturbations.

Solutions with T-horizons are unstable.

Conditions for horizon existence are rigorously established.

Abstract

Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional gravity with a chain of $n$ Ricci-flat internal spaces are considered, with the Maxwell field potential having two nonzero components: the temporal, Coulomb-like one and the one pointing to one of the extra dimensions. The properties and special cases of the solutions are discussed, in particular, those when there are horizons in the space-time. Two types of horizons are distinguished: the conventional black-hole (BH) ones and those at which the physical section of the space-time changes its signature (the latter are called {\it T-horizons}). Two theorems are proved, one fixing the BH- and T-horizon existence conditions, the other claiming that the system under study cannot have a regular center. The stability of a selected family of solutions under spherically symmetric perturbations is studied. It is shown that only black-hole solutions are stable, while all others, in particular, those with T-horizons are unstable.