Supergravity S-Branes

TL;DR

The paper addresses the construction and classification of space-like (S-brane) solutions in supergravity. It employs solution-generating dualities applied to an 11D vacuum Einstein solution with $R_{AB}=0$ to produce SD$p$-branes, NS-brane space-branes, and M-theory S-branes, including bound states. It provides explicit constructions of SD0, SD$p$, SF-string, SNS5-brane, SM2-brane, and SM5-brane solutions, and analyzes their far-field and near-brane behavior, highlighting singularities and special horizon cases. The work broadens the spectrum of time-dependent string backgrounds and informs potential holographic interpretations and M-theory resolutions, while identifying persistent singularities as a major challenge and guiding future investigations into worldvolume theories and boundary conditions.

Abstract

We construct supergravity solutions corresponding to space-like branes in string theory. Our approach is to apply the usual solution generating techniques to an appropriate time-dependent solution of the eleven dimensional vacuum Einstein equations. In this way all SDp-brane solutions are obtained, as well as the NS and M-theory space branes. Bound states of SDp/SD(p-2)- and SDp/SD(p-4)-branes are also constructed. Finally, we begin an investigation of the near-brane regions and singularity structure of these solutions.

Figures (3)

• Figure 1: Flat space parametrization appropriate for the construction described in the text.
• Figure 2: The Penrose diagram for the solutions (\ref{['boso']}) with the special choice of exponents given in eq. (\ref{['bhcase']}). Two asymptotically flat regions (at $t\rightarrow\infty$ and $t\rightarrow0$) are joined by a throat. The horizons (at $t=\omega$, $z=\pm\infty$) in the throat region surround time-like singularities (at $T\rightarrow0$).
• Figure 3: The function ${\cal{R}}_p(n)$, as a function of ${n},p$ for ${m}>0$ and ${m}<0$ respectively. (The edges of the surfaces occur where $n$ runs out due to the reality constraint on $m$.)