Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 8

Construction of Cauchy data for the dynamical formation of apparent horizons and the Penrose Inequality

Pages: 2379 – 2496

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n8.a1

Authors

Nikolaos Athanasiou (Department of Mathematics, Oxford University, Oxford, United Kingdom)

Martin Lesourd (Black Hole Initiative, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

Based on scale critical initial data, we construct smooth asymptotically flat Cauchy initial data for the Einstein vacuum system that does not contain Marginally Outer Trapped Surfaces (MOTS) but whose future evolution contains a trapped region, which itself is bounded by an apparent horizon (a smooth hypersurface foliated by MOTS).

Using estimates for the ADM mass of the data and the area of the MOTS foliating the apparent horizon, this construction yields a dynamical setting in which to study the spacetime Penrose Inequality. We show that the inequality holds in an open region in the future of the initial data, which itself can be controlled by the parameters of the initial data.

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Published 5 January 2024