Aberrational Effects for Shadows of Black Holes

TL;DR

This paper derives an analytical formula for the shadow boundary of a Kerr black hole as seen by a moving observer, highlighting how observer motion affects the shadow's appearance.

Contribution

It introduces a new analytical expression for black hole shadow boundaries accounting for observer motion, enhancing understanding of observational effects.

Findings

Derived an explicit formula for shadow boundary with observer motion

Visualized shadow variations for different observer velocities

Showed how observer motion influences shadow shape and size

Abstract

In this paper, we discuss how the shadow of a Kerr black hole depends on the motion of the observer. In particular, we derive an analytical formula for the boundary curve of the shadow for an observer moving with given four-velocity at given Boyer--Lindquist coordinates. We visualize the shadow for various values of parameters.