Gravitational hedgehog, stringy hedgehog and stringy sphere

TL;DR

This paper explores various solutions to Einstein's equations involving hedgehog configurations and their matching conditions, revealing the formation of stringy shells and their deviations under different matchings.

Contribution

It introduces new matching solutions of Einstein equations with hedgehog configurations, analyzing conditions leading to stringy shells and their deviations.

Findings

Hedgehog solutions can be matched to form stringy shells.

Matching conditions influence the shell's stringy character.

Deviations occur when matching more general solutions.

Abstract

We investigate the solutions of Einstein equations such that a hedgehog solution is matched to different exterior or interior solutions via a spherical shell. In the case where both the exterior and the interior regions are hedgehog solutions or one of them is flat, the resulting spherical shell becomes a stringy shell. We also consider more general matchings and see that in this case the shell deviates from its stringy character.