Derives a factorized leading term for the strong deflection angle near degenerate photon spheres using local expansion of the effective potential and Weyl tensor measures.
Hod, On the number of light rings in curved spacetimes of ultra-compact objects (2017), arXiv:1710.00836 [gr-qc]
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In a very interesting paper, Cunha, Berti, and Herdeiro have recently claimed that ultra-compact objects, self-gravitating horizonless solutions of the Einstein field equations which have a light ring, must possess at least {\it two} (and, in general, an even number of) light rings, of which the inner one is {\it stable}. In the present compact paper we explicitly prove that, while this intriguing theorem is generally true, there is an important exception in the presence of degenerate light rings which, in the spherically symmetric static case, are characterized by the simple dimensionless relation $8\pi r^2_{\gamma}(\rho+p_{\text{T}})=1$ [here $r_{\gamma}$ is the radius of the light ring and $\{\rho,p_{\text{T}}\}$ are respectively the energy density and tangential pressure of the matter fields]. Ultra-compact objects which belong to this unique family can have an {\it odd} number of light rings. As a concrete example, we show that spherically symmetric constant density stars with dimensionless compactness $M/R=1/3$ possess only {\it one} light ring which, interestingly, is shown to be {\it unstable}.
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In dRGT massive gravity, static spherically symmetric black holes exhibit zero, one, or two photon spheres whose topological charges and stability patterns differ from Einstein gravity and from horizonless compact objects.
Surface-gravity waves in shallow water can be configured with central and graded drainage to analogize regular black holes and mimickers, enabling lab study of their instabilities.
citing papers explorer
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Strong-deflection expansion of the deflection angle near a degenerate photon sphere
Derives a factorized leading term for the strong deflection angle near degenerate photon spheres using local expansion of the effective potential and Weyl tensor measures.
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Topological charge and black hole photon spheres in massive gravity
In dRGT massive gravity, static spherically symmetric black holes exhibit zero, one, or two photon spheres whose topological charges and stability patterns differ from Einstein gravity and from horizonless compact objects.
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Analog regular black holes and black hole mimickers for surface-gravity waves in fluids
Surface-gravity waves in shallow water can be configured with central and graded drainage to analogize regular black holes and mimickers, enabling lab study of their instabilities.