A class of solutions to the conformal constraint equations on compact manifolds with apparent horizon boundary conditions

2022/10/18 by Pailleron, Jean-David
#35Q75 #53C21 (Primary) #53C80 #83C05 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2210.09823

Abstract

This article is dedicated to solving the Einstein constraint equations with apparent horizon boundaries and freely specified mean curvature. The main novelty is that we study the conformal constraint equations assuming only low regularity.

Related

• Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries
• The Einstein Constraint Equations on Asymptotically Euclidean Manifolds
• Uniform Estimates for the Constant Mean Curvature Solutions of the Vacuum Einstein Constraint Equations on Compact Manifolds
• Exploring the Conformal Constraint Equations
• The Constraint Equations