Singularities in geodesic surface congruence

TL;DR

This paper explores singularities in geodesic surface congruences within stringy cosmology, deriving Raychaudhuri equations with string-specific corrections and establishing conditions under which singularities inevitably occur.

Contribution

It introduces modified Raychaudhuri equations for strings, incorporating string-specific correction terms, and demonstrates the universality of the strong energy condition's implications for singularities.

Findings

Stringy strong energy conditions lead to a Hawking-Penrose type inequality.

Negative initial expansion results in inevitable singularity passage.

Both time-like and null string congruences satisfy the same inequality.

Abstract

In the stringy cosmology, we investigate singularities in geodesic surface congruences for the time-like and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the time-like and null string congruences produce the same inequality equation.