Fetching the paper…
Reading the bibliography…
Photon surfaces are timelike, totally umbilic hypersurfaces of Lorentzian spacetimes.
Richard Arnowitt, Stanley Deser, and Charles W. Misner, Coordinate Invariance and Energy Expressions in General Relativity , Phys. Rev. 122
1961
Earlier work this paper cites.
F. R. Tangherlini, Schwarzschild field in n n dimensions and the dimensionality of space problem , Nuovo Cim. 27
1963
Earlier work this paper cites.
Werner Israel, Event Horizons in Static Vacuum Space-Times , Phys. Rev. 164
1967
Earlier work this paper cites.
Richard M. Schoen and Shing-Tung Yau, On the Proof of the Positive Mass Conjecture in General Relativity , Comm. Math. Phys. 65
1979
Earlier work this paper cites.
Edward Witten, A new proof of the positive energy theorem , Comm. Math. Phys. 80
1981
Earlier work this paper cites.
Gary L. Bunting and Abdul Kasem Muhammad Masood-ul Alam, Nonexistence of multiple black holes in asymptotically Euclidean static vacuum space-time , General Relativity and Gravitation 19
1987
Earlier work this paper cites.
Daniel Kennefick and Niall Ó Murchadha, Weakly decaying asymptotically flat static and stationary solutions to the Einstein equations , Class. Quantum Grav. 12
1995
Earlier work this paper cites.
Markus Heusler, Black Hole Uniqueness Theorems , Cambridge Lecture Notes in Physics, Camb. Univ. Press, 1996
1996
Earlier work this paper cites.
Alessandra Buonanno and Thibault Damour, Effective one-body approach to general relativistic two-body dynamics , Phys. Rev. D 59
1999
Earlier work this paper cites.
Clarissa-Marie Claudel, Kumar Shwetketu Virbhadra, and George F. R. Ellis, The Geometry of Photon Surfaces , J. Math. Phys. 42
2001
Earlier work this paper cites.
Gary W. Gibbons, Daisuke Ida, and Tetsuya Shiromizu, Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions , Progr. Theoret. Phys. Suppl. (2002), no. 148, 284–290
2002
Earlier work this paper cites.
Pengzi Miao, Positive Mass Theorem on Manifolds admitting Corners along a Hypersurface , Adv. Theor. Math. Phys. 6
2002
Cited alongside, same era.
Thomas Foertsch, Wolfgang Hasse, and Volker Perlick, Inertial forces and photon surfaces in arbitrary spacetimes , Classical Quantum Gravity 20
2003
Cited alongside, same era.
Volker Perlick, On totally umbilic submanifolds of semi-Riemannian manifolds , Nonlinear Analysis 63
2005
Cited alongside, same era.
David Robinson, Four decades of black hole uniqueness theorems , The Kerr spacetime: Rotating black holes in General Relativity (SM Scott DL Wiltshire, M. Visser, ed.), Cambridge University Press, 2009, pp. 115–143
2009
Cited alongside, same era.
Gary W. Gibbons and Claude M. Warnick, Aspherical photon and anti-photon surfaces , Physics Letters B 763
2016
Later among the works it cites.
Virginia Agostiniani and Lorenzo Mazzieri, On the Geometry of the Level Sets of Satic Potentials , Communications in Mathematical Physics 355
2017
Later among the works it cites.
2017
Later among the works it cites.
Andrey A. Shoom, Metamorphoses of a photon sphere , Phys. Rev. D 96
2017
Later among the works it cites.
Yoshimune Tomikawa, Tetsuya Shiromizu, and Keisuke Izumi, On the uniqueness of the static black hole with conformal scalar hair , PTEP. Prog. Theor. Exp. Phys. (2017), no. 3, 033E03, 8
2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2012
Cited alongside, same era.
Donovan McFeron and Gábor Székelyhidi, On the positive mass theorem for manifolds with corners , Communications in Mathematical Physics 313
2012
Cited alongside, same era.
2014
Cited alongside, same era.
Carla Cederbaum, Uniqueness of photon spheres in static vacuum asymptotically flat spacetimes , Complex Analysis & Dynamical Systems VI, Contemp. Math, vol. 667, AMS, 2015, pp. 86–99
2015
Cited alongside, same era.
Stoytcho S. Yazadjiev, Uniqueness of the static spacetimes with a photon sphere in Einstein-scalar field theory , Phys. Rev. D 91
2015
Cited alongside, same era.
Stoytcho S. Yazadjiev and Boian Lazov, Uniqueness of the static Einstein–Maxwell spacetimes with a photon sphere , Classical Quantum Gravity 32
2015
Cited alongside, same era.
Carla Cederbaum and Gregory J. Galloway, Uniqueness of photon spheres in electro-vacuum spacetimes , Classical Quantum Gravity 33
2016
Cited alongside, same era.
Hirotaka Yoshino, Uniqueness of static photon surfaces: Perturbative approach , Phys. Rev. D 95
2017
Later among the works it cites.
Sophia Jahns, Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes , Classical and Quantum Gravity 36
2019
Closest in time.
Carla Cederbaum, Sophia Jahns, and Olivia Vičánek Martínez, On equipotential photon surfaces in electrostatic spacetimes of arbitrary dimension , in preparation, 2020
2020
Closest in time.
Carla Cederbaum and Markus Wolff, Some new perspectives on the Kruskal–Szekeres extension with applications to photon surfaces , in preparation, 2020
2020
Closest in time.