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July 2018 The intersection of a hyperplane with a lightcone in the Minkowski spacetime
Pengyu Le
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J. Differential Geom. 109(3): 497-507 (July 2018). DOI: 10.4310/jdg/1531188194

Abstract

Klainerman, Luk and Rodnianski derived an anisotropic criterion for formation of trapped surfaces in vacuum, extending the original trapped surface formation theorem of Christodoulou. The effort to understand their result led us to study the intersection of a hyperplane with a lightcone in the Minkowski spacetime. For the intrinsic geometry of the intersection, depending on the hyperplane being spacelike, null or timelike, it has the constant positive, zero or negative Gaussian curvature. For the extrinsic geometry of the intersection, we find that it is a noncompact marginal trapped surface when the hyperplane is null. In this case, we find a geometric interpretation of the Green’s function of the Laplacian on the standard sphere. In the end, we contribute a clearer understanding of the anisotropic criterion for formation of trapped surfaces in vacuum.

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Pengyu Le. "The intersection of a hyperplane with a lightcone in the Minkowski spacetime." J. Differential Geom. 109 (3) 497 - 507, July 2018. https://doi.org/10.4310/jdg/1531188194

Information

Received: 24 May 2016; Published: July 2018
First available in Project Euclid: 10 July 2018

zbMATH: 06917315
MathSciNet: MR3825609
Digital Object Identifier: 10.4310/jdg/1531188194

Rights: Copyright © 2018 Lehigh University

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Vol.109 • No. 3 • July 2018
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