Image of the time-dependent black hole

TL;DR

This paper models the time-dependent evolution of a Vaidya black hole's image, showing how the observable flux and features like faculae change over time due to increasing mass, aligning with recent observational variability reports.

Contribution

It introduces a conformal Vaidya metric with a linearly increasing mass function and analyzes the resulting black hole image evolution using semi-analytical ray tracing methods.

Findings

Facula undergoes radial displacement over time

Observable flux evolves with the new time coordinate

Black hole image features are time-dependent

Abstract

The Event Horizon Telescope's 2024 observations report a shift in the position angle of the brightness asymmetry in M87*, revealing time variability in the black hole's image. In this analysis, we investigate the time-dependent of a Vaidya black hole. By introducing a mass function that increases linearly with time, along with a conformal transformation, we derive the conformal Vaidya metric and define a new time coordinate $t_c$. Using the semi-analytical approach, we analyze the ray trajectories and radiation flux of the Vaidya black hole in the background of a thin accretion disk. We discuss how the observed flux in the Vaidya spacetime evolves as a function of the new time coordinate $t_c$. The results show that the facula on the observable plane undergoes radial displacement as $t_c$ increases, revealing the time-dependent evolution of black hole images.