Analytical calculation of black hole spin using deformation of the shadow

Abstract

We succeed to find compact analytical expressions which allow to easily extract the black hole spin from observations of its shadow, without need to construct or model the entire curve of the shadow. The deformation of Kerr black hole shadow can be characterized in a simple way by oblateness (the ratio of the horizontal and vertical angular diameters which are supposed to be measured by an observer). The deformation is significant in case the black hole is nearly extreme and observer is not so far from the equatorial plane. In this approximation, we present: (i) the spin lower limit via oblateness, (ii) the spin via oblateness and viewing angle, in case the latter is known from other observations.

Black Hole Parameter Estimation from Its Shadow

“…Though the shape of shadow is determined by the properties of null geodesics, it is neither the Euclidean image of its horizon nor of its photon region, rather it is the gravitationally lensed image of photon region. that their applicability is limited to a specific class of shadows demanding some symmetries in their shapes, and may not precisely work for black hole in some modified theories of gravity [43], which leads to the introduction of new observables [39,[41][42][43][50][51][52][53]. Here, we would like to develop new observables for the characterization of the black hole shadow.…”

“…The subscript r, l, t, and b respectively stand for right, left, top, and bottom of shadow silhouette. For spherically symmetric black hole shadow D = 1, whilst for a Kerr shadow √ 3/2 ≤ D < 1 [41]. The oblateness parameter can be identified as the measure of distortion in a shadow.…”

Gravitational lensing of a star by a rotating black hole

“…[30][31][32][33][34][35][36][37]. The existence of black holes in the Universe can be proved for the first time in a direct experiment.This will simultaneously provide an experimental strong field test of not only the general relativity but also many other theories of gravity, e.g., f (R), C 2 , Galilean, Horndeski, mimetic, and multidimensional (see, e.g., [38][39][40][41][42][43][44][45][46][47][48][49][50]). The next qualitatively new stage of investi- gations will be a detailed study of the shape of the shadow of the SgrA* black hole, as well as the features of motion of objects around it, e.g., individual stars and compact gas clouds [51][52][53][54][55][56][57][58][59][60][61].…”

Upper bound on the GUP parameter using the black hole shadow

“…Following Refs. [3,[50][51][52], let us construct two observables for the black hole shadow. The first one indicates the difference between the x and y axes.…”