Anisotropic Einstein data with isotropic nonnegative scalar curvature
Differential Geometry
2012-07-12 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We construct a black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of initial data contained inside the black hole. The constraints translate into a parabolic equation, with radius as "time" variable, on a metric component u that undergoes blow up. The metric itself is regular up to and including the surface at blow up radius, which is a minimal surface. By applying equivariant bifurcation theory on a self similarly rescaled equation, we show the existence of blow up profiles that are not O(3) symmetric - or anisotropic - although the curvature was isotropically prescribed.
Keywords
Cite
@article{arxiv.1207.2116,
title = {Anisotropic Einstein data with isotropic nonnegative scalar curvature},
author = {Bernold Fiedler and Juliette Hell and Brian Smith},
journal= {arXiv preprint arXiv:1207.2116},
year = {2012}
}