Time dependent supergravity solutions in arbitrary dimensions

TL;DR

This paper derives time-dependent supergravity solutions in arbitrary dimensions with specific symmetries, exploring their properties, extremality conditions, and relations to known brane solutions in string theories.

Contribution

It provides new explicit time-dependent supergravity solutions with symmetries ISO(p+1)×SO(d-p-2,1) in arbitrary dimensions, including non-extremal and non-BPS cases, and relates them to existing brane solutions.

Findings

Solutions include magnetically charged Euclidean or space-like branes.

Extremality leads to imaginary magnetic charges and type II* branes.

Non-extremal solutions match known solutions in 10 dimensions.

Abstract

By directly solving the equations of motion we obtain the time dependent solutions of supergravities with dilaton and a $q$-form field-strength in arbitrary dimensions. The metrics are assumed to have the symmetries ISO($p+1$) $\times$ SO($d-p-2,1$) and can be regarded as those of the magnetically charged Euclidean or space-like branes. When we impose the extremality condition, we find that the magnetic charges of the branes become imaginary and the corresponding real solutions then represent the E$p$-branes of type II$^\ast$ theories (for the field-strengths belonging to the RR sector). On the other hand, when the extremality condition is relaxed we find real solutions in type II theories which resemble the solutions found by Kruczenski-Myers-Peet. In $d=10$ they match exactly. We point out the relations between the solutions found in this paper and those of Chen-Gal'tsov-Gutperle in arbitrary dimensions. Although there is no extremal limit for these solutions, we find another class of solutions, which resemble the solutions in the extremal case with imaginary magnetic charges and the corresponding real solutions can be regarded as the non-BPS E$p$-brane solutions of type II$^\ast$ theories (for the field-strengths in RR sector).