Spacelike spherically symmetric CMC hypersurfaces in Schwarzschild spacetimes (I): Construction
Kuo-Wei Lee, Yng-Ing Lee
TL;DR
This paper constructs and analyzes spacelike spherically symmetric constant mean curvature hypersurfaces in Schwarzschild spacetimes, exploring their behavior near the horizon and extending them smoothly in Kruskal coordinates.
Contribution
It provides a systematic method for constructing complete SS-CMC hypersurfaces in Schwarzschild spacetime and examines their asymptotic and smooth properties.
Findings
Explicit solutions near the horizon r=2M
Extension of hypersurfaces in Kruskal coordinates
Smoothness properties of the constructed hypersurfaces
Abstract
We solve spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in Schwarzschild spacetimes and analyze their asymptotic behavior near the coordinate singularity r = 2M. Furthermore, we join SS-CMC hypersurfaces in the Kruskal extension to obtain complete ones and discuss the smooth properties.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Black Holes and Theoretical Physics