Metamorphoses of a photon sphere

Abstract

There are circular planar null geodesics at r = 3M around a Schwarzschild black hole of mass M . These geodesics form a photon sphere. Null geodesics of the Schwarzschild space-time which do not form the photon sphere are either escape to null infinity or get captured by the black hole. Thus, from the dynamical point of view, the photon sphere represents a smooth basin boundary that separates the basins of escape and capture of the dynamical system governing the null geodesics. Here we consider a Schwarzschild black hole distorted by an external, static, and axisymmetric quadrupolar gravitational field defined by a quadrupole moment q. We study null geodesics around such a black hole and show that the photon sphere does not survive the distortion. For q −0.017001 it transforms into a fractal basin boundary that indicates chaotic behavior of the null geodesics. We calculate the box-counting fractal dimension of the basin boundary and the related uncertainty exponent, which depend on the value of the quadrupole moment.

Applications of Spatial Technology in Schistosomiasis Control Programme in The People's Republic of China

“…While, blue and green points correspond to trajectories escaped from the black hole in the upward and downward directions, respectively. Obviously, the basin boundary near the photon sphere possesses some fractal structures, which is similar to that obtained in the distorted Schwarzschild black hole [62]. From Fig.…”

Understanding photon sphere and black hole shadow in dynamically evolving spacetimes

“…This effect can in principle be observed from Earth, providing a definitive test of existence of black holes and for this very purpose, the Event Horizon telescope is being designed to observe the shadow like structure around the supermassive object at the center of our galaxy [42][43][44][45]. Various other interesting aspects of photon sphere and shadow has been extensively studied by numerous authors [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62]. However, black holes are in general not stationary since they continuously accrete matter and grow in size.…”

Geometry and topology of the Kerr photon region in the phase space

“…For static spacetimes, trapping of light has turned out to be a useful tool to prove uniqueness theorems; a static, asymptotically flat vacuum spacetime with a photon sphere as its inner boundary has to be a Schwarzschild spacetime [1,3]; analogous results holds for some cases with matter [2,25,26,27], and for one case even perturbative uniqueness was established [28], see also [20,21].…”