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Uniqueness of photon spheres in electro-vacuum spacetimes · Around

2015

Uniqueness of photon spheres in electro-vacuum spacetimes

Cederbaum, Carla, Galloway, Gregory J.

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In a recent paper, the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam's proof of static vacuum black hole uniqueness.

Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asymptotically flat spacetimes by adapting the argument of Masood-ul-Alam.
As a consequence of our result, we can rule out the existence of electrostatic configurations involving multiple "very compact" electrically charged bodies and sub-extremal black holes.

Built on

David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order , 2 ed., Springer, 1970
1970
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.
Abdul Kasem Muhammad Masood-ul Alam, Uniqueness proof of static charged black holes revisited , Class. Quantum Grav. 9
1992
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.

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Clarissa-Marie Claudel, Kumar Shwetketu Virbhadra, and George F. R. Ellis, The Geometry of Photon Surfaces , J. Math. Phys. 42
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Carla Cederbaum, Uniqueness of photon spheres in static vacuum asymptotically flat spacetimes , arXiv:1406.5475v1, 2014
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Gregory J Galloway and Pengzi Miao, Variational and rigidity properties of static potentials , arXiv:1412.1062
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Carla Cederbaum and Gregory J. Galloway, Uniqueness of photon spheres via positive mass rigidity , arXiv:1504.05804v1
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Then

Dan A Lee and Philippe G LeFloch, The positive mass theorem for manifolds with distributional curvature , arXiv:1408.4431
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Later among the works it cites.
Stoytcho S. Yazadjiev, Uniqueness of the static spacetimes with a photon sphere in Einstein-scalar field theory , arXiv:1501.06837v1
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Stoytcho S. Yazadjiev and Boian Lazov, Uniqueness of the static spacetimes with a photon sphere in Einstein-scalar field theory , arXiv:1503.06828v1
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