Light from Schwarzschild Black Holes in de Sitter expanding universe

TL;DR

This paper introduces an algebraic method to derive the redshift and shadow of a moving Schwarzschild black hole in a de Sitter universe, providing general formulas and specific cases for observational predictions.

Contribution

The paper presents a novel algebraic approach to calculate black hole redshifts and shadows in an expanding universe, extending previous methods to include peculiar velocities.

Findings

Derived general expressions for black hole redshift and shadow in de Sitter space.

Provided particular case analyses and intuitive expansions.

Developed an algebraic code for complete results.

Abstract

A new method is applied for deriving the redshift and shadow of a Schwarzschild black hole moving freely in the de Sitter expanding universe as recorded by a co-moving remote observer. This method is manly algebraic focusing on the transformation of the conserved quantities under the de Sitter isometry relating the black hole proper co-moving frame to observer's one. Hereby one extracts the general expressions of the redshifts and shadows of the black holes having peculiar velocities but their expressions are too extended to be written down here. Therefore, only some particular cases and intuitive expansions are presented while the complete results are given in an algebraic code on computer \cite{Comp}.