On supergravity solutions of space-like Dp-branes

TL;DR

This paper compares two supergravity solutions for space-like Dp-branes, showing how boundary conditions relate their parameters and how they can be transformed into each other through coordinate changes and dualities.

Contribution

It demonstrates the equivalence of two different supergravity solutions under specific boundary conditions and transformations, clarifying their relationship.

Findings

CGG and KMP solutions are related through boundary conditions.

Both solutions can be mapped to each other via coordinate transformation and duality.

Parameter relations between the two solutions are established.

Abstract

Recently the time dependent solutions of type II supergravities in $d = 10$, with the metric having the symmetry $ISO(p+1) \times SO(8-p, 1)$ have been given by two groups (Chen-Gal'tsov-Gutperle (CGG), [hep-th/0204071] and Kruczenski-Myers-Peet (KMP), [hep-th/0204144]). The supergravity solutions correspond to space-like D$p$-branes in type II string theory. While the CGG solution is a four parameter solution, the KMP solution is a three parameter solution and so in general they are different. This difference can be attributed to the fact that unlike the CGG solution, KMP uses a specific boundary condition for the metric and the dilaton field. It is shown that when we impose the boundary conditions used in the KMP solution to the CGG solution then both become three parameter solutions and they map to each other under a coordinate transformation along with a Hodge duality of the field strength. We also give the relations between the parameters characterizing the two solutions.