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arXiv · 1207.2116

Anisotropic Einstein data with isotropic nonnegative scalar curvature

Bernold Fiedler·Juliette Hell·Brian Smith
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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.

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BibTeXRIS

Bernold Fiedler, Juliette Hell, Brian Smith. 2012-07-11. Anisotropic Einstein data with isotropic nonnegative scalar curvature. https://arxiv.org/abs/1207.2116

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