Exactly solvable gravitating perfect fluid solitons in (2+1) dimensions

TL;DR

This paper analytically solves a gravitating baby Skyrme model in (2+1) dimensions, revealing BPS properties in flat space and exploring solutions in de Sitter and anti-de Sitter backgrounds, with implications for holographic QCD.

Contribution

It demonstrates the complete analytical solvability of a self-gravitating BPS baby Skyrme model in flat space and explores solutions in curved spacetimes, including exact multi-soliton solutions in AdS.

Findings

BPS property preserved in flat space-time

Mass-radius relation derived analytically

Existence of extremal and non-extremal solutions in curved backgrounds

Abstract

The Bogomolnyi-Prasad-Sommerfield (BPS) baby Skyrme model coupled to gravity is considered. We show that in an asymptotically flat space-time the model still possesses the BPS property, i.e., admits a BPS reduction to first order Bogomolnyi equations, which guarantees that the corresponding proper energy is a linear function of the topological charge. We also find the mass-radius relation as well as the maximal mass and radius. All these results are obtained in an analytical manner, which implies the complete solvability of this selfgravitating matter system. If a cosmological constant is added, then the BPS property is lost. In de Sitter (dS) space-time both extremal and non-extremal solutions are found, where the former correspond to finite positive pressure solutions of the flat space-time model. For the asymptotic anti-de Sitter (AdS) case, extremal solutions do not exist as there are no negative pressure BPS baby Skyrmions in flat space-time. Non-extremal solutions with AdS asymptotics do exist and may be constructed numerically. The impact of the negative cosmological constant on the mass-radius relation is studied. We also found two potentials for which exact multi-soliton solutions in the external AdS space can be obtained. Finally, we elaborate on the implications of these findings for certain three-dimensional models of holographic QCD.