More on general $p$-brane solutions

TL;DR

This paper analyzes and generalizes the classification of static $p$-brane solutions in Einstein-dilaton-antisymmetric form theories, identifying new solutions like black walls and relating them to existing solutions with extra parameters.

Contribution

It extends the uniqueness classification of $p$-brane solutions to partially delocalized cases and introduces new solutions such as black walls, connecting them to recent solutions with additional parameters.

Findings

Two main classes of solutions: asymptotically flat black $p$-branes and non-flat $p$-branes with linear dilaton background.

Generalization of the uniqueness argument to partially delocalized branes.

Discovery of black wall solutions in the codimension one case.

Abstract

Recently it was found that the complete integration of the Einstein-dilaton-antisymmetric form equations depending on one variable and describing static singly charged $p$-branes leads to two and only two classes of solutions: the standard asymptotically flat black $p$-brane and the asymptotically non-flat $p$-brane approaching the linear dilaton background at spatial infinity. Here we analyze this issue in more details and generalize the corresponding uniqueness argument to the case of partially delocalized branes. We also consider the special case of codimension one and find, in addition to the standard domain wall, the black wall solution. Explicit relations between our solutions and some recently found $p$-brane solutions ``with extra parameters'' are presented.