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Utilizing concepts from dynamical systems theory, we demonstrate how the existence of light rings, or fixed points, in a spacetime will give rise to families of periodic orbits and invariant manifolds in phase space.
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Configuration III from [ 24 ]
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The compactified radial coordinate X X is defined as X = X ∗ 1 + X ∗ , X ∗ = r 2 − r h 2 X=\frac{X^{*}}{1+X^{*}},\quad X^{*}=\sqrt{r^{2}-r_{h}^{2}} , where r h r_{h} is the horizon radius of the black hole
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