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Uniqueness of static photon surfaces: Perturbative approach · Around

2016

Uniqueness of static photon surfaces: Perturbative approach

Yoshino, Hirotaka

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A photon surface $S$ is defined as a three-dimensional timelike hypersurface such that any null geodesic initially tangent to $S$ continues to be included in $S$, like $r=3M$ of the Schwarzschild spacetime.

Using analytic solutions to static perturbations of a Schwarzschild spacetime, we examine whether a nonspherical spacetime can possess a distorted static photon surface.
It is shown that if the region outside of $r=3M$ is vacuum, no distorted photon surface can be present.
Therefore, we establish the perturbative uniqueness for an asymptotically flat vacuum spacetime with a static photon surface.

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