Sobolev spaces for multi-black hole initial data

Abstract

In this article we introduce weighted Sobolev spaces that are well suited to treat initial data for multiple black hole systems. We prove general results for elliptic operators on these spaces and give a simple proof of existence of a class of initial data describing many extremal black holes.

13 pages, no figures

References in corpus (4)

• Rough Solutions of the Einstein Constraint Equations on Compact Manifolds
• Construction of N-body initial data sets in general relativity
• Extreme throat initial data set and horizon area--angular momentum inequality for axisymmetric black holes
• Rough Solutions of the Einstein Constraint Equations