Spinning straight cosmic strings with flat exterior solutions generically violate the weak energy condition

TL;DR

This paper demonstrates that spinning cosmic strings with flat exterior solutions inherently violate the weak energy condition, indicating fundamental limitations in their theoretical models within general relativity.

Contribution

It proves that any interior solution for such spinning cosmic strings must violate the weak energy condition, highlighting a fundamental constraint in modeling these objects.

Findings

Interior solutions violate weak energy condition

Adding mass introduces exterior gravitational field

Constraints on modeling spinning cosmic strings

Abstract

Any interior solution for a cylindrically symmetric, stationary cosmic string with flat exterior, spinning around its longitudinal axis, and without internal longitudinal currents ($g_{zz}=1$, $g_{tz}=0$), must somewhere violate the weak energy condition of standard general relativity. Existing interior solutions may be readily fixed by adding mass to the string above that generating its angular deficit, but at the cost of introducing an exterior gravitational field.