Obstructions to the existence of solutions of the self-dual Einstein-Maxwell-Higgs equations on a compact surface
Analysis of PDEs
2022-01-11 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
In this note we present an obstruction to the existence of solutions to the self-dual Einstein-Maxwell-Higgs equations on a compact surface, which depends on the multiplicities of the zeroes of the \emph{Higgs field} and the \emph{vortex number} . In particular, we exhibit infinitely many examples of Higgs fields for which solutions cannot exist.
Keywords
Cite
@article{arxiv.2201.03455,
title = {Obstructions to the existence of solutions of the self-dual Einstein-Maxwell-Higgs equations on a compact surface},
author = {Luis Álvarez-Cónsul and Mario Garcia-Fernandez and Oscar García-Prada and Vamsi Pritham Pingali and Chengjian Yao},
journal= {arXiv preprint arXiv:2201.03455},
year = {2022}
}
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11 pages