From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to the last photon orbit. With simple numerical and a...
On the other hand, we consider the non-radial motion of a free-falling test particle, in the equatorial plane, from spatial infinity to the black hole. In the ultrarelativistic limit, we show that the photon sphere acts as an effective Rindler horizon for the geodesic motion of the test ...
Thus, the instabilities of photon circular trajectories, delimiting the black hole photon-sphere, are double exponentialized. Specifically we individuate two Lyapunov exponents, rather than only one, related to two different sources of chaos in geodesic orbits as a sort of butterfly effect. Such a...
Li, The shadow and photon sphere of the charged black hole in Rastall gravity. Class. Quantum Gravity 38, 165013 (2021) ADS MathSciNet Google Scholar L. Ma, H. Lü, Bounds on Photon Spheres and Shadows of Charged Black Holes in Einstein-Gauss-Bonnet-Maxwell Gravity. Phys. Lett. B ...
1、Black Holes,Black Holes,The intense gravitational field left when a giant star collapses,It is called a black hole because not even light can escape,Photon Sphere,The outer edge where light bends but is still escapable,Event Horizon,The point at which no light can escape,Singularity,The sh...
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existence of highly compact objects consistent with black holes [13, 14]. However, some physicists argue that while these observations confirm the presence of objects with incredibly strong gravitational fields and a photon sphere, they do not definitively prove the existence of singularities [15, ...
It is well known that, for the lensing by a black hole, an infinite number of Einstein rings are formed by the light rays which wind around the black hole nearly on the photon sphere, which are called relativistic Einstein rings. This is also the case for the lensing by a wormhole. In...
For the observers of the black hole’s “shadow”, it is perhaps the photon sphere that is the most important quantity. Provided the so-called “null energy condition” holds. Angular scales in this context are mostly given in fractions of arcseconds, i.e., milliarcseconds (mas) or micro...
where, for convenience, we introduce the ‘reduced’ charge q related to the total charge Q by \(q=\frac{4\pi }{S_3}Q\) in which \(S_3=2\pi ^2\) is the volume of the unit 3-sphere. The electrostatic potential \(A_t(r)\) of the black hole is obtained as $$\begin{alig...