Exact solutions in gravity with a sigma model source

TL;DR

This paper derives exact cosmological and black hole solutions in a higher-dimensional gravity model coupled with non-linear scalar fields, revealing new classes of solutions and a restricted no-hair theorem.

Contribution

It provides explicit solutions in a multidimensional gravity-sigma model framework, including cosmological, spherically symmetric, and soliton solutions, extending previous results.

Findings

Exact cosmological solutions with Ricci-flat factor spaces

A subclass of spherically symmetric solutions and a no-hair theorem

Identification of latent soliton solutions for d_1=2

Abstract

We consider a D-dimensional model of gravity with non-linear "scalar fields" as a matter source. The model is defined on the product manifold M, which contains n Einstein factor spaces. General cosmological type solutions to the field equations are obtained when n-1 factor spaces are Ricci-flat, e.g. when one space M_1 of dimension d_1 > 1 has nonzero scalar curvature. The solutions are defined up to solutions to geodesic equations corresponding to a sigma model target space. Several examples of sigma models are presented. A subclass of spherically-symmetric solutions is studied and a restricted version of "no-hair theorem" for black holes is proved. For the case d_1 =2 a subclass of latent soliton solutions is singled out.