Analytical calculation of black hole spin using deformation of the shadow

We succeed to find compact analytical expressions which allow one 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 the 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 the 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.

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