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In a recent paper the first author established the uniqueness of photon spheres, suitably defined, in static vacuum asymptotically flat spacetimes by adapting Israel's proof of static black hole uniqueness.
Werner Israel, Event Horizons in Static Vacuum Space-Times , Phys. Rev. 164
1967
Earlier work this paper cites.
David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order , 2 ed., Springer, 1970
1970
Earlier work this paper cites.
Henning Müller zum Hagen, The static two body problem , Proc. Camb. Phil. Soc. 75
1974
Earlier work this paper cites.
Robert M. Wald, General Relativity , The University of Chicago Press, 1984
1984
Earlier work this paper cites.
Robert Bartnik, The Mass of an Asymptotically Flat Manifold , Communications on Pure and Applied Mathematics 39
1986
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.
Clarissa-Marie Claudel, Kumar Shwetketu Virbhadra, and George F. R. Ellis, The Geometry of Photon Surfaces , J. Math. Phys. 42
2001
Cited alongside, same era.
Volker Perlick, On totally umbilici submanifolds of semi-Riemannian manifolds , Nonlinear Analysis 63
2005
Cited alongside, same era.
Lars Andersson and Bernd G. Schmidt, Static self-gravitating many-body systems in Einstein gravity , Class. Quant. Grav. 26
2009
Cited alongside, same era.
Robert Beig and Richard M. Schoen, On static n n -body configurations in relativity. , Class. Quant. Grav. 26
2009
Cited alongside, same era.
Theodore Frankel, Gravitational Curvature: An Introduction to Einstein’s Theory , Dover Books on Physics, 2011
2011
Cited alongside, same era.
2012
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2014
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2014
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2014
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