TY - JOUR

T1 - Anisotropic Einstein data with isotropic non negative prescribed scalar curvature

AU - Fiedler, Bernold

AU - Hell, Juliette

AU - Smith, Brian

N1 - Funding Information:
This work was supported by the Deutsche Forschungsgemeinschaft, SFB 647 “Space–Time–Matter” .
Publisher Copyright:
© 2014 Elsevier Masson SAS. All rights reserved.

PY - 2015/3/1

Y1 - 2015/3/1

N2 - We construct time-symmetric black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of such initial data contained inside the black hole. In this case, the Einstein constraint equations translate into a parabolic equation, with radius as 'time' variable, for a metric component u that undergoes blow up. The metric itself is regular up to and including the surface at the blow up radius, which is a minimal surface. We show the existence of Einstein constrained data with blow up profiles that are anisotropic (i.e. not O(3) symmetric) although the scalar curvature was isotropically prescribed. Our results are based on center manifold theory for quasilinear parabolic equations and on equivariant bifurcation theory for not necessarily self-similar solutions of a self-similarly rescaled equation.

AB - We construct time-symmetric black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of such initial data contained inside the black hole. In this case, the Einstein constraint equations translate into a parabolic equation, with radius as 'time' variable, for a metric component u that undergoes blow up. The metric itself is regular up to and including the surface at the blow up radius, which is a minimal surface. We show the existence of Einstein constrained data with blow up profiles that are anisotropic (i.e. not O(3) symmetric) although the scalar curvature was isotropically prescribed. Our results are based on center manifold theory for quasilinear parabolic equations and on equivariant bifurcation theory for not necessarily self-similar solutions of a self-similarly rescaled equation.

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U2 - 10.1016/j.anihpc.2014.01.002

DO - 10.1016/j.anihpc.2014.01.002

M3 - Article

AN - SCOPUS:84926102358

VL - 32

SP - 401

EP - 428

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

SN - 0294-1449

IS - 2

ER -