Bogomol'nyi Bounds for Gravitational Cosmic Strings

TL;DR

This paper introduces a new method to establish lower energy bounds for gravitational cosmic string solutions, extending the traditional Bogomol'nyi approach to include asymmetric solutions and applicable across the entire solution space.

Contribution

It generalizes the Bogomol'nyi procedure to gravitational theories, providing bounds valid for all solutions and allowing for asymmetric bound-saturating solutions.

Findings

New method produces universal bounds for cosmic strings in gravity

Method extends Bogomol'nyi bounds to asymmetric solutions

Applicable to models where traditional bounds are limited

Abstract

We present a new method for finding lower bounds on the energy of topological cosmic string solutions in gravitational field theories. This new method produces bounds that are valid over the entire space of solutions, unlike the traditional approach, where the bounds obtained are only valid for cylindrically symmetric solutions. This method is shown to be a generalisation of the well-known Bogomol'nyi procedure for non-gravitational theories and as such, it can be used to find gravitational Bogomol'nyi bounds for models wherever the traditional Bogomol'nyi procedure can be applied in the non-gravitational limit. Furthermore, this method yields Bogomol'nyi equations that do not rule out the existence of asymmetric bound-saturating solutions.