A first-order formalism for timelike and spacelike brane solutions

TL;DR

This paper extends the formalism of first-order BPS-type equations to include both timelike and spacelike brane solutions, encompassing stationary and time-dependent cases in various dimensions.

Contribution

It introduces a unified first-order formalism for timelike and spacelike branes, including non-extremal and time-dependent solutions, broadening the scope of BPS equation applications.

Findings

Derived fake/pseudo-BPS equations for all stationary branes.

Extended formalism to time-dependent branes in arbitrary dimensions.

Applicable to Einstein-dilaton-p-form systems.

Abstract

We show that the construction of BPS-type equations for non-extremal black holes due to Miller et. al. can be extended to branes of arbitrary dimension and, more importantly, to time-dependent solutions. We call these first-order equations fake- or pseudo-BPS equations in light of the formalism that has been developed for domain wall and cosmological solutions of gravity coupled to scalar fields. We present the fake/pseudo-BPS equations for all stationary branes (timelike branes) and all time-dependent branes (spacelike branes) of an Einstein-dilaton-p-form system in arbitrary dimensions.