Shape and position of the shadow in the $\delta = 2$ Tomimatsu-Sato space-time

Abstract

Within 5-10 years, very long baseline interferometry facilities will be able to observe the "shadow" of super-massive black hole candidates. This will allow, for the first time, to test gravity in the strong field regime. In this paper, we study numerically the photon orbits in the $\delta = 2$ Tomimatsu-Sato space-time. The $\delta = 2$ Tomimatsu-Sato space-time is a stationary, axisymmetric, and asymptotically flat exact solution of the vacuum Einstein equations. We compare the associated shadow with the one of Kerr black holes. The shape of the shadow in the $\delta = 2$ Tomimatsu-Sato space-time is oblate and the difference between the two axes can be as high as 6% when viewed on the equatorial plane. We argue that future space sub-mm interferometers (e.g. VSOP-3) may distinguish the two cases, and thus are able to test the Cosmic Censorship Conjecture.