Chaotic Shadows of Black Holes: A Short Review

Abstract

We give a brief review on the formation and the calculation of black hole shadow. Firstly, we introduce the conception of black hole shadow and the current works on a variety of black hole shadows. Secondly, we present main methods of calculating photon sphere radius and shadow radius, and then explain how the photon sphere affect the boundary of black hole shadow. We review the analytical calculation for black hole shadows which have analytic expressions for shadow boundary due to the integrable photon motion system. And we introduce the fundamental photon orbits which can explain the patterns of black hole shadow shape. Finally, we review the numerical calculation of black hole shadows with the backward ray-tracing method, and introduce some chaotic black hole shadows with self-similar fractal structures. Since the gravitational waves from the merger of binary black holes have been detected, we introduce a couple of shadows of binary black holes, which all have the eyebrowlike shadows around the main shadows with the fractal structures. We discuss the invariant phase space structures of photon motion system in black hole space-time, and explain the formation of black hole shadow is dominated by the invariant manifolds of certain Lyapunov orbits near the fixed points.

Shape of higher-order images of equatorial emission rings around a Schwarzschild black hole: Analytical description with polar curves

“…In 2019, the Event Horizon Telescope has been presented the shadow of supermassive black hole in the M87 galaxy [59][60][61][62][63][64][65][66][67] (see also recent results about Sgr A* [68][69][70][71][72][73]). After that, attention has been attracted to the study of higher-order photon rings which can be expected in a more detailed image, being concentrated near the edge of the black hole shadow [74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92]. These rings are lensed images of the luminous matter surrounding the black hole.…”

Note on fundamental physics tests from black hole imaging: Comment on "Hunting for extra dimensions in the shadow of Sagittarius A$^*$"

“…Millimeter-scale Very Long Baseline Interferometry (VLBI) has recently provided us with the first horizon-scale images of supermassive black holes (BHs): these feature a central brightness depression, related to the underlying BH shadow [1,2], surrounded by a bright ring of emission. In most scenarios, the BH shadow corresponds to the apparent image of the photon region, the region of space-time where photons are forced to travel along orbits [3][4][5]. Modifications to General Relativity, the presence of additional fields, as well as violations of fundamental principles, typically leave imprints on the BH shadow: horizon-scale BH images can thus be used to test fundamental physics, provided the size of the bright ring can be used as a proxy for the shadow size r sh , with little dependence on the details of the accretion flow, which is the case for the geometrically thick, optically thin, radiatively inefficient accretion flows surrounding both M87 * and Sagittarius A * (Sgr A * ) [6][7][8][9][10][11][12][13].…”