Trajectories of light beams in a Kerr metric: the influence of the rotation of an observer on the shadow of a black hole

TL;DR

This paper analyzes how the rotation of an observer affects the shape of a black hole's shadow by studying light trajectories in a Kerr spacetime using Hamiltonian dynamics.

Contribution

It introduces a classification of light trajectories and derives boundary relations for the black hole shadow for rotating observers.

Findings

Bifurcation diagram of light trajectories constructed

Classification of trajectory types based on first integrals

Boundary relations for black hole shadow derived for rotating observers

Abstract

This paper investigates the trajectories of light beams in a Kerr metric, which describes the gravitational field in the neighborhood of a rotating black hole. After reduction by cyclic coordinates, this problem reduces to analysis of a Hamiltonian system with two degrees of freedom. A bifurcation diagram is constructed and a classification is made of the types of trajectories of the system according to the values of first integrals. Relations describing the boundary of the shadow of the black hole are obtained for a stationary observer who rotates with an arbitrary angular velocity about the axis of rotation of the black hole.