Shadows of Kerr-Vaidya-like black holes

TL;DR

This paper analyzes the shadow boundaries of rotating, time-dependent black holes with well-defined limits, providing an analytic formula for the shadow shape and exploring its relation to accretion rates and observations.

Contribution

It introduces a new class of Kerr-Vaidya-like black hole solutions with analytic shadow boundary formulas, linking theoretical models to observational data.

Findings

Derived an analytic formula for shadow boundaries of these black holes.

Found a power law relating shadow size and asymmetry to accretion rate.

Discussed applicability to EHT observations of M87* and Sgr A*.

Abstract

In this work, we study the shadow boundary curves of rotating time-dependent black hole solutions which have well-defined Kerr and Vaidya limits. These solutions are constructed by applying the Newman-Janis algorithm to a spherically symmetric seed metric conformal to the Vaidya solution with a mass function that is linear in Eddington-Finkelstein coordinates. Equipped with a conformal Killing vector field, this class of solution exhibits separability of null geodesics, thus allowing one to develop an analytic formula for the boundary curve of its shadow. We find a simple power law describing the dependence of the mean radius and asymmetry factor of the shadow on the accretion rate. Applicability of our model to recent Event Horizon Telescope observations of M87${}^*$ and Sgr A${}^*$ is also discussed.