Shadow of Kottler black hole in the presence of plasma for a co-moving observer

TL;DR

This paper analyzes the shadow of a Kottler black hole in a plasma environment from a co-moving observer's perspective, examining how cosmological constant and plasma affect shadow size, and constrains plasma parameters using observations of M87* and Sgr A*.

Contribution

It provides a detailed analysis of black hole shadow size in Kottler spacetime with plasma, incorporating co-moving coordinates and observational data to constrain plasma parameters.

Findings

Cosmological constant and plasma significantly influence shadow size.

Derived shadow radius for co-moving observers in Kottler spacetime.

Constrained plasma parameter using observational data of M87* and Sgr A*.

Abstract

We consider a spherically symmetric black hole metric in (3+1)-dimensions in presence of a positive cosmological constant $\Lambda$. We use a general approach as proposed in \cite{1} to transform the metric in co-moving coordinates. Then for a general metric we have evaluated the angular shadow size both in absence and presence of plasma. By using the aberration relation, we then find the corresponding shadow radius as viewed by a co-moving observer for Schwarzschild de-Sitter or Kottler spacetime. The effect of cosmological constant $\Lambda$ and plasma parameter $k$ on the angular size of black hole shadow has been observed in detail. Finally, by using the observed angular size of M87$^*$ and Sgr A$^*$ black hole, we constrain the value of the plasma parameter $k$ with a specific observational value of the cosmological constant $\Lambda$ (or the Hubble constant $H_0$).