http://arxiv.org/abs/2201.01946
We demonstrate that the location of a stable photon sphere (PS) in a compact object is not always an edge such as the inner boundary of a black hole shadow, whereas the location of an unstable PS is known to be the shadow edge notably in the Schwarzschild black hole. If there exists the outermost stable PS in a static spherically symmetric (SSS) spacetime, the spacetime is not asymptotically flat. A nondivergent deflection is caused for a photon traveling around a stable PS, though a logarithmic divergent behavior is known to appear in most of SSS compact objects with an unstable photon sphere. The reason for the nondivergence is that the closest approach of a photon is prohibited in the immediate vicinity of the stable PS when the photon is emitted from a source (or reaches a receiver) distant from a lens object. The finite gap size depends on the receiver and source distances from the lens as well as the lens parameters. The mild deflection angle of light can be approximated by an arcsine function. A class of SSS solutions in Weyl gravity exemplifies the nondivergent deflection near the stable outer PS.
R. Kudo and H. Asada
Fri, 7 Jan 22
27/34
Comments: 9 pages, 4 figures
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