Uniqueness of static photon surfaces: Perturbative approach

Abstract

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. It is also pointed out that if matter is present in the outside region, there is a possibility that a distorted photon surface could form.

16 pages, no figure, title slightly changed, discussion added as Sec.III, published version

References in corpus (3)

• Can strong gravitational lensing distinguish naked singularities from black holes?
• New nonuniform black string solutions
• Uniqueness of the static spacetimes with a photon sphere in Einstein-scalar field theory

Cited by in corpus (5)

• Aspherical Photon and Anti-Photon Surfaces
• Completing characterization of photon orbits in Kerr and Kerr-Newman metrics
• Metamorphoses of a photon sphere
• Divergence equations and uniqueness theorem of static spacetimes with conformal scalar hair
• Loosely trapped surface and dynamically transversely trapping surface in Einstein-Maxwell system