The Positive Mass Theorem for Creased Initial Data

2025/08/25 by Kazaras, Demetre, Khuri, Marcus, Lin, Michael
#53C21 #83C99 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2508.17585

Abstract

We establish a spacetime positive mass theorem and rigidity statement for asymptotically flat spin initial data sets with a codimension one singularity controlled by a matching Bartnik data condition involving spacetime rotations, and discuss applications. This generalizes several previous works on the topic, including results of Miao, Tsang, and Shi-Tam.

Citations

• Initial data sets with vanishing mass are contained in pp-wave spacetimes
• The case of equality for the spacetime positive mass theorem
• On a spacetime positive mass theorem with corners
• Mass of asymptotically flat 3-manifolds with boundary
• Bartnik mass minimizing initial data sets and improvability of the dominant energy scalar
• Spacetime Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Initial Data for the Einstein Equations
• Lorentzian positive mass theorem for spacetimes with distributional curvature
• The Higher Dimensional Positive Mass Theorem II
• A positive mass theorem for low-regularity Riemannian metrics
• Boundary conditions at spatial infinity from a Hamiltonian point of view
• A positive mass theorem for Lipschitz metrics with small singular sets
• The spacetime positive mass theorem in dimensions less than eight
• Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature
• The mass of an asymptotically flat manifold
• A new proof of the positive energy theorem
• On the proof of the positive mass conjecture in general relativity

Related

• A tilted spacetime positive mass theorem
• Positive mass theorems for spin initial data sets with arbitrary ends and dominant energy shields
• Tilted spacetime positive mass theorem with arbitrary ends
• On a spacetime positive mass theorem with corners
• Initial data rigidity implies spacetime rigidity