Spacelike spherically symmetric CMC hypersurfaces in Schwarzschild spacetimes (I): Construction

2011/11/11 by Kuo-Wei Lee, Lee, Kuo-Wei, Yng-Ing Lee +1
Mathematics · Physics and Astronomy · #83C15 (Primary) 83C05 (Secondary) #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #gr-qc #math-ph #math.DG #math.MP #msc:83C05 #msc:83C15

paper · pdf · doi:10.48550/arxiv.1111.2679

32 pages, 10 figures

openalex publication_date 2011/11/11 · arxiv created 2011/12/07 · arxiv updated 2011/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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.

Related

• Boundary behaviors of spacelike constant mean curvature surfaces in Schwarzschild spacetime
• Spacelike CMC surfaces near null infinity of the Schwarzschild spacetime
• Existence of CMC Cauchy surfaces and spacetime splitting
• Existence of Constant Mean Curvature Hypersurfaces in Asymptotically Flat Spacetimes
• Remarks on the existence of CMC Cauchy surfaces