Understanding photon sphere and black hole shadow in dynamically evolving spacetimes

Abstract

We have derived the differential equation governing the evolution of the photon sphere for dynamical black hole spacetimes with or without spherical symmetry. Numerical solution of the same depicting evolution of the photon sphere has been presented for Vaidya, Reissner-Nordström-Vaidya and de-Sitter Vaidya spacetimes. It has been pointed out that evolution of the photon sphere depends crucially on the validity of the null energy condition by the in-falling matter and may present an observational window to even test it through black hole shadow. We have also presented the evolution of the photon sphere for slowly rotating Kerr-Vaidya spacetime and associated structure of black hole shadow. Finally, the effective graviton metric for Einstein-Gauss-Bonnet gravity has been presented, and the graviton sphere has been contrasted with the photon sphere in this context. * akash.mishra@iitgn.ac.in

The evolutions of the innermost stable circular orbits in dynamical spacetimes

“…Below, We will use two simple examples to demonstrate the reliability of our method. In the Vaidya case, we get a reasonable evolution curve which is similar to the evolution curve of photon sphere in [30], and a similar curve is also obtained in Vaidya-AdS4 spacetime.…”

“…: V,-vol slow rotation limit of Kerr-Vaidya spacetime. The results given by these examples are reasonable and can be compared with the evolutions of the photon spheres in dynamical spacetimes [30]. So, we believe that this generalization is reliable.…”

“…In the slow rotation limit, the 4-dimensional Kerr-Vaidya metric on the equatorial plane can be expressed as [30,45]…”

Null geodesics, quasinormal modes, and the correspondence with shadows in high-dimensional Einstein-Yang-Mills spacetimes

“…For the evolution of photon spheres in dynamical black hole spacetimes and the connection to shadows, please refer to Ref [31]…”

Ergosphere, Photon Region Structure, and the Shadow of a Rotating Charged Weyl Black Hole

“…These methods were later developed and generalized widely (see [80][81][82][83][84][85]). Having these methods in hand, a large number of black hole spacetimes, including those with cosmological components, were given rigorous analytical calculations, simulations, numerical, and observational studies [86][87][88][89][90][91][92][93][94][95][96][97][98][99][100]. The black hole shadow is of great importance as it provides information about the light propagation in near-horizon regions.…”