Anisotropic Einstein data with isotropic nonnegative scalar curvature

2012/07/09 by Bernold Fiedler, Fiedler, Bernold, Juliette Hell +3
Mathematics · Physics and Astronomy · #53 #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.DS #math.MP #msc:53

paper · pdf · doi:10.48550/arxiv.1207.2116

openalex publication_date 2012/07/09 · arxiv created 2012/07/11 · arxiv updated 2012/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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