Shape and position of the shadow in the δ = 2 Tomimatsu–Sato spacetime

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 us, for the first time, to test gravity in the strong field regime. In this paper, we numerically study the photon orbits in the δ = 2 Tomimatsu–Sato spacetime. The δ = 2 Tomimatsu–Sato spacetime 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 δ = 2 Tomimatsu–Sato spacetime 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.

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