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

TL;DR

This paper numerically analyzes the shadow shape of the $\,\delta=2$ Tomimatsu-Sato space-time, comparing it with Kerr black holes, and discusses the potential of future interferometers to distinguish these models and test the Cosmic Censorship Conjecture.

Contribution

It provides the first detailed numerical comparison of the black hole shadow in the $\,\delta=2$ Tomimatsu-Sato space-time with that of Kerr black holes, highlighting observable differences.

Findings

The shadow in the $\,\delta=2$ Tomimatsu-Sato space-time is oblate.

The difference in axes can reach up to 6% in the equatorial view.

Future interferometers could distinguish these space-times, testing the Cosmic Censorship Conjecture.

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.