Plane waves with weak singularities

Abstract

We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which do not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity.

22 pages, Added references and clarifying comments

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• Global Fluctuation Spectra in Big Crunch/Big Bang String Vacua
• A Matrix Model for the Null-Brane
• Quantum evolution across singularities: the case of geometrical resolutions
• String spectra near some null cosmological singularities
• Can free strings propagate across plane wave singularities?
• Null cosmological singularities and free strings: II
• Null cosmological singularities and free strings
• Power-law singularities in string theory and M-theory
• String Excitation by Initial Singularity of Inflation
• On the breakdown of the perturbative interaction picture in Big Crunch/Big Bang or the true reason why perturbative string amplitudes on temporal orbifolds diverge