2023/11/29 by Carla Cederbaum, Cederbaum, Carla, Sophia Jahns +3 · 2 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #Equipotential #Equipotential surface #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical analysis #Mathematical physics #Mathematics #Photon #Photon sphere #Physics #Quantum Electrodynamics and Casimir Effect #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Relativity and Gravitational Theory #Schwarzschild radius #Spacetime #Spherically symmetric spacetime #Uniqueness
paper · pdf · doi:10.48550/arxiv.2311.17509
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/11/29 · openalex created_date 2023/12/01 · openalex updated_date 2026/08/01
We study timelike, totally umbilic hypersurfaces -- called photon surfaces -- in n+1-dimensional static, asymptotically flat spacetimes, for n+1≥4. First, we give a complete characterization of photon surfaces in a class of spherically symmetric spacetimes containing the (exterior) subextremal Reissner--Nordström spacetimes, and hence in particular the (exterior) positive mass Schwarzschild spacetimes. Next, we give new insights into the spacetime geometry near equipotential photon surfaces and provide a new characterization of photon spheres (not appealing to any field equations). We furthermore show that any asymptotically flat electrostatic electro-vacuum spacetime with inner boundary consisting of equipotential, (quasi-locally) subextremal photon surfaces and/or non-degenerate black hole horizons must be isometric to a suitable piece of the necessarily subextremal Reissner--Norström spacetime of the same mass and charge. Our uniqueness result applies work by Jahns and extends and complements several existing uniqueness theorems. Its proof fundamentally relies on the lower regularity rigidity case of the Riemannian Positive Mass Theorem.