The effective sigma-model of multidimensional gravity

TL;DR

This paper analyzes the effective sigma-model in multidimensional gravity, exploring its geometric properties, solutions with scalar fields, and the impact of brane intersections on black hole thermodynamics.

Contribution

It introduces new solutions with scalar fields that can induce inflation in multiple spatial directions and examines the role of the Einstein frame in cosmological models.

Findings

Existence of exact solutions under the orthobrane condition.

Scalar fields can cause inflation in additional spatial dimensions.

T_H depends on p-brane intersection dimensions.

Abstract

The properties of the effective sigma-model for D-dimensional Einstein gravity based on multidimensional geometries is analyzed. Besides pure geometry, additional minimally coupled scalars and (p+2)-forms are considered which yield an extended target space after reduction to the effective D_0-dimensional geometry. In any case the target space is a homogeneous space. The orthobrane condition guarantees the existence of exact solutions. Geometrically, it makes the target space a locally symmetric one. New solutions with scalar fields are found, which may inflate not only in time-like but in also in additional spatial directions of the effective geometry. Static spherically symmetric solutions with a particular configuration of intersecting electric and magnetic branes are investigated both, for the orthobrane case and for degenerated charges. In both cases T_H depends critically on the intersection dimension of the p-branes. Finally, the role of the Einstein frame for 4-geometries is addressed, and the physical frame transformation for cosmological geometries is given.