First analytical calculation of black hole shadow in McVittie metric

TL;DR

This paper derives the first analytical expression for the size of a black hole shadow in an expanding universe described by the McVittie metric, accounting for cosmic expansion effects.

Contribution

It provides the first analytical solution for black hole shadow size in the McVittie metric for any observer position and expansion law, using matched asymptotic expansions.

Findings

Analytical formula for shadow size in McVittie metric derived

Solution valid for arbitrary observer positions and expansion laws

Examples include de Sitter and matter-dominated universes

Abstract

Cosmic expansion influences the angular size of black hole shadow. The most general way to describe a black hole embedded into an expanding universe is to use the McVittie metric. So far, the exact analytical solution for the shadow size in the McVittie metric, valid for arbitrary law of expansion and arbitrary position of the observer, has not been found. In this paper, we present the first analytical solution for angular size of black hole shadow in McVittie metric as seen by observer comoving with the cosmic expansion. We use a method of matched asymptotic expansions to find approximate solution valid within the entire range of possible positions of observer. As two particular examples, we consider black hole in de Sitter and matter dominated universe.