Exactly solvable gravitating perfect fluid solitons in (2+1) dimensions
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.
Keywords
Cite
@article{arxiv.1802.07278,
title = {Exactly solvable gravitating perfect fluid solitons in (2+1) dimensions},
author = {C. Adam and T. Romanczukiewicz and M. Wachla and A. Wereszczynski},
journal= {arXiv preprint arXiv:1802.07278},
year = {2018}
}
Comments
Latex file, 34 pages, 13 figures, v2: conclusions on the stability of AdS Skyrmions weakened, results and remaining conclusions unchanged