Exact solutions in multidimensional gravity with antisymmetric forms

TL;DR

This paper reviews exact solutions in a multidimensional gravity model with scalar fields and antisymmetric forms, focusing on p-brane configurations and their various spacetime geometries.

Contribution

It provides a comprehensive overview of the sigma-model approach and exact solutions involving p-branes in multidimensional gravity with scalar and form fields.

Findings

Classified solutions include Majumdar-Papetrou-type, cosmological, spherically symmetric, black-brane, and Freund-Rubin-type.

Demonstrated the applicability of the sigma-model approach to find exact solutions.

Analyzed the structure of solutions on manifolds composed of Einstein spaces.

Abstract

This topical review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the form M = M_0 x M_1 x ...x M_n, where M_i are Einstein spaces (i >0). The sigma-model approach and exact solutions in the model are reviewed and the solutions with p-branes (e.g. Majumdar-Papapetrou-type, cosmological, spherically symmetric, black-brane and Freund-Rubin-type ones) are considered.