Electric S-brane solutions with a parallel charge density form on a Ricci-flat factor space

TL;DR

This paper extends S-brane solutions in higher-dimensional gravity to Ricci-flat spatial geometries, characterizing solutions with self-dual or anti-self-dual charge forms that exist in specific dimensions and include additional Ricci-flat factor-spaces.

Contribution

It generalizes previous flat-space S-brane solutions to Ricci-flat geometries and incorporates non-brane Ricci-flat factor-spaces, revealing new solution classes in higher-dimensional gravity.

Findings

Solutions exist only in dimensions D=4m+1 with specific p-values.

Charge density forms are self-dual or anti-self-dual with positive square.

Inclusion of Ricci-flat factor-spaces broadens the solution landscape.

Abstract

We generalize the previously studied cosmological solutions in D-dimensional gravity with an antisymmetric (p+2)-form to the case when the spatial part of the metric is Ricci-flat rather than flat. These generalized solutions are characterized by a parallel self-dual or anti-self-dual charge density form Q of rank 2m and satisfy the condition Q^2 >0. As with the previous flat-space case, these electric, S-brane solutions only exist when D=4m+1 = 5, 9, 13, ... and p= 2m -1 = 1, 3, 5, .... We further generalize these solutions by adding Ricci-flat factor-spaces which are not covered by branes.