PT2 - Gravitational lensing and shadows |
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Speaker |
Cederbaum, Carla |
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| Talk Title |
Static, equipotential photon surfaces have no hair |
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Abstract |
The Schwarzschild spacetime is well-known to possess a unique “photon sphere” – meaning a cylindrical, timelike hypersurface P such that any null geodesic initially tangent to P remains tangent to P – in all dimensions. We will show that it also possesses a rich family F of spatially spherically symmetric “photon surfaces” – general timelike hypersurfaces P such that any null geodesic initially tangent to P remains tangent to P. This generalizes a result of Foertsch, Hasse, and Perlick from 2+1 to higher dimensions. Moreover, we investigate the existence and properties of photon surfaces in a large class of static, spherically symmetric spacetimes. We show that they are (almost) necessarily rotationally symmetric. We will also present a general theorem that implies that any static, vacuum, asymptotically flat spacetime possessing a so-called “equipotential” photon surface must already be the Schwarzschild spacetime. The proof of the theorem uses and extends Riemannian geometry arguments first introduced by Bunting and Masood-ul-Alam in their proof of static black hole uniqueness. It holds in all dimensions n+1>3+1. Part of this work is joint with Gregory J. Galloway. |
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