Power-law singularities in string theory and M-theory

TL;DR

This paper generalizes power-law singularities to supergravity, string, and M-theory, analyzing their geometries, exponents, and Penrose limits, and proposes tests for resolving singularities within these theories.

Contribution

It extends the concept of power-law singularities to advanced theories and investigates their geometries, exponents, and potential resolutions.

Findings

Near singularity geometries characterized by Kasner exponents

Penrose limits exhibit profiles with specific power-law behavior

Proposed tests for singularity resolution in string and M-theory

Abstract

We extend the definition of the Szekeres-Iyer power-law singularities to supergravity, string and M-theory backgrounds, and find that are characterized by Kasner type exponents. The near singularity geometries of brane and some intersecting brane backgrounds are investigated and the exponents are computed. The Penrose limits of some of these power-law singularities have profiles $A\sim {\rm u}^{-\gamma}$ for $\gamma\geq 2$. We find the range of the exponents for which $\gamma=2$ and the frequency squares are bounded by 1/4. We propose some qualitative tests for deciding whether a null or timelike spacetime singularity can be resolved within string theory and M-theory based on the near singularity geometry and its Penrose limits.