The positive mass theorem with angular momentum and charge for manifolds with boundary

2018/06/30 by Edward T. Bryden, Marcus A. Khuri, Benjamin D. Sokolowsky
Mathematics · Physics and Astronomy · #Angular momentum #Angular momentum operator #Boundary (topology) #Charge (physics) #Conjecture #Cosmic censorship hypothesis #Cosmology and Gravitation Theories #Curvature #Gas Dynamics and Kinetic Theory #Geometric Analysis and Curvature Flows #Scalar (mathematics) #Scalar curvature #gr-qc #math-ph #math.DG #math.MP

paper · pdf · doi:10.1063/1.5070080

published as J. Math. Phys., 60 (2019), no. 5, 052501, 10 pp

openalex created_date 2018/07/10 · openalex publication_date 2019/05/01 · arxiv created 2021/01/25 · arxiv updated 2021/01/26 · openalex updated_date 2026/08/06

Abstract

Motivated by the cosmic censorship conjecture in mathematical relativity, we establish the precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of angular momentum and charge. In particular, this result does not require the restrictive assumptions of simple connectivity and completeness, which are undesirable from both a mathematical and physical perspective.

Citations

• On the proof of the positive mass conjecture in general relativity
• A new proof of the positive energy theorem
• Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass
• Stability and rigidity of extremal surfaces in Riemannian geometry and General Relativity