Does the shape of the shadow of a black hole depend on motional status of an observer?

TL;DR

This paper investigates how the apparent shape and size of black hole shadows vary with the observer's motion, revealing that shadows of spherical black holes remain circular but are size-shrunk by motion, while Kerr black hole shadows depend on observer motion.

Contribution

It introduces a distortion parameter for black hole shadows and analyzes the effects of observer motion on shadow shape and size in a unified framework.

Findings

Spherical black hole shadows are circular for all observers.

Shadow size shrinks for moving observers, not due to length contraction.

Kerr black hole shadows depend on observer motion, never appearing perfectly circular.

Abstract

In a recent work on rotating black hole shadows [Phys. Rev. D{\bf 101}, 084029 (2020)], we proposed a new approach for calculating size and shape of the shadows in terms of astrometrical observables with respect to finite-distance observers. In this paper, we introduce a distortion parameter for the shadow shapes and discuss the appearance of the shadows of static spherical black holes and Kerr black holes in a uniform framework. We show that the shape of the shadow of a spherical black hole is circular in the view of arbitrary observers, and the size of the shadows tends to be shrunk in the view of a moving observer. The diameter of the shadows is contracted even in the direction perpendicular to the observers' motion. This seems not to be understood as length contraction effect in special relativity. The shape of Kerr black holes is dependent on motional status of observers located at finite distance. In spite of this, it is found that there is not a surrounding observer who could view the shape of the Kerr black hole shadows as circularity. These results could be helpful for observation of the Sagittarius A* in the centre of the Milky Way, as our solar system is moving around the centre black hole.