Null Geodesics and Observational Signatures of Kerr Naked Singularities

The Event Horizon Telescope (EHT) recently resolved the supermassive black hole at the center of M87 at the event horizon scale. The reconstructed black hole images show asymmetric rings with interior brightness depressions. This result was used to test modified gravity theories by constraining how the black hole spacetime may deviate from the Kerr solution with black hole spin |a| < 1. This range of the black hole spin was assumed because of the weak cosmic censorship hypothesis, which states that singularities need to be hidden from an observer at infinity by an event horizon. In this work, we propose to use the EHT images to test the weak cosmic censorship hypothesis. We assume the Kerr spacetime is correct for simplicity but relax the spin assumption by surveying a wide range of black holes from spin |a| < 1 to spin |a| > 1. We perform a detailed study on the null geodesics surrounding Kerr naked singularities, including spherical photon orbits and chaotic regions. From the simulations, we predict the structure of the "black hole shadow" and observable signatures of naked singularities. By comparing these predictions with current and future EHT observations, we can test the weak cosmic censorship hypothesis in the Kerr solution.