Instability of a Kerr-type naked singularity due to light and matter accretion and its shadow

TL;DR

This paper investigates the stability and observational features of over-spinning Kerr-type naked singularities, showing that accretion can lead to horizon formation, and analyzing their shadows compared to black holes.

Contribution

It demonstrates that accretion causes naked singularities to develop horizons, and compares their shadows with those of Kerr black holes, highlighting observational indistinguishability.

Findings

Naked singularities become hidden under horizons after accretion.

Shadows of naked singularities are similar to Kerr black holes from certain viewpoints.

Retrograde accretion reduces the spin parameter, leading to horizon formation.

Abstract

We study null and timelike constant radii geodesics in the environment of an over-spinning putative Kerr-type naked singularity. We are particularly interested in two topics: first, the differences of the shadows of the naked rotating singularity and the Kerr black hole; and second, the spinning down effect of the particles falling from the accretion disk. Around the naked singularity, the non-equatorial prograde orbits in the Kerr black hole remain intact up to a critical rotation parameter ($\alpha=\sqrt{6 \sqrt{3}-9}$) and cease to exist above this value [Eur. Phys. J. C 78, 879 (2018)]. This has an important consequence in the shadow of the naked singularity if the shadow is registered by an observer on the polar plane or close to it as the shadow cannot be distinguished from that of a Kerr black hole viewed from the same angle considering only the light emanating from the unstable photon orbits. We show that the timelike retrograde orbits in the equatorial plane immediately (after about an 8% increase in mass for the case of initial $\alpha=1.5$) reduce the spin parameter of the naked singularity from larger values to $\alpha=1$ at which an event horizon appears. This happens because the retrograde orbits have a larger capture cross-section than the prograde ones. So if a naked singularity happens to have an accretion disk, it will not remain naked for long, an event horizon forms.