Volume preserving spacetime mean curvature flow and foliations of initial data sets

2024/07/17 by Jacopo Tenan, Tenan, Jacopo
Physics and Astronomy · #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2407.12971

Abstract

We consider a volume preserving curvature evolution of surfaces in an asymptotically Euclidean initial data set with positive ADM-energy. The speed is given by a nonlinear function of the mean curvature which generalizes the spacetime mean curvature recently considered by Cederbaum-Sakovich (Calc. Var. PDE, 2021). Following a classical approach by Huisken-Yau (Invent. Math., 1996), we show that the flow starting from suitably round initial surfaces exists for all times and converges to a constant (spacetime) curvature limit. This provides an alternative construction of the CSTMC foliation by Cederbaum-Sakovich and has applications in the definition of center of mass of an isolated system in General Relativity.

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