Gravity of higher-dimensional global defects

TL;DR

This paper derives solutions to Einstein's equations for higher-dimensional global defects with a cosmological constant, revealing diverse geometries including flat, inflating, and warped spacetimes, and discusses their quantum nucleation processes.

Contribution

It provides new exact solutions for higher-dimensional global defects with a cosmological constant, extending previous models to include inflating and warped geometries.

Findings

Solutions include flat brane worlds with a deficit angle for Lambda=0

Inflating brane solutions for Lambda > 0

Warped geometries similar to Randall-Sundrum models for Lambda < 0

Abstract

Solutions of Einstein's equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant Lambda. The defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field configuration in the n extra dimensions. For Lambda = 0 and n > 2, the solutions are characterized by a flat brane worldsheet and a solid angle deficit in the extra dimensions. For Lambda > 0, one class of solutions describes spherical branes in an inflating higher-dimensional universe. Instantons obtained by a Euclidean continuation of such solutions describe quantum nucleation of the entire inflating brane-world, or of a spherical brane in an inflating higher-dimensional universe. For Lambda < 0, one class of solutions exhibits an exponential warp factor. It is similar to spacetimes previously discussed by Randall and Sundrum for n = 1 and by Gregory for n = 2.