The Universality of Penrose Limits near Space-Time Singularities

TL;DR

This paper demonstrates that Penrose limits near power-law space-time singularities exhibit a universal behavior, with implications for string theory modes and their potential extension through singularities.

Contribution

It proves the universality of Penrose limits near power-law singularities under certain energy conditions, and relates these limits to string mode extensions.

Findings

Penrose limits show a universal u^{-2} behaviour near singularities.

Oscillator frequencies allow for analytic extension of string modes.

Results apply to metrics satisfying the dominant energy condition.

Abstract

We prove that Penrose limits of metrics with arbitrary singularities of power-law type show a universal leading u^{-2}-behaviour near the singularity provided that the dominant energy condition is satisfied and not saturated. For generic power-law singularities of this type the oscillator frequencies of the resulting homogeneous singular plane wave turn out to lie in a range which is known to allow for an analytic extension of string modes through the singularity. The discussion is phrased in terms of the recently obtained covariant characterisation of the Penrose limit; the relation with null geodesic deviation is explained in detail.