Positive mass theorem for asymptotically flat spin manifolds with isolated conical singularities

2023/10/20 by Xianzhe Dai, Dai, Xianzhe, Yukai Sun +3 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2310.13285

openalex publication_date 2023/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There has been a lot of interests in Positive Mass Theorems for singular metrics on smooth manifolds. We prove a positive mass theorem for asymptotically flat (AF) spin manifolds with isolated conical singularities or more generally horn singularities. In particular, we allow topological singularities in the space as we do not require the cross sections of the conical singularity to be spherical. Note that the negative mass Schwarzschild metric is AF with a horn singularity.

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