Gravitational effect of a plasma on the shadow of Schwarzschild black holes

TL;DR

This paper investigates how a fully ionized plasma influences the shadow of Schwarzschild black holes, finding that under realistic conditions, both effects are negligible, but gravitational effects can dominate in supermassive black holes.

Contribution

It provides a unified formalism to analyze both refractive and gravitational effects of plasma on black hole shadows, highlighting their relative insignificance in realistic scenarios.

Findings

Corrections to shadow radius are negligible for realistic parameters.

Gravitational correction can surpass refractive correction for black holes larger than 10^9 solar masses.

Refractive effects are negligible compared to gravitational effects in typical astrophysical conditions.

Abstract

Considering a Schwarzschild black hole surrounded by a fully ionized hydrogen plasma, we study the refractive effect and the pure gravitational effect of the plasma on the shadow. The effects are treated in a unified formalism but characterized by two independent parameters. For semi-realistic values of parameters, we find their corrections to the shadow radius are both negligible, and the gravitational correction can overtake the refractive correction for active galactic nuclei of masses larger than $10^9M_{\odot}$. Since the refractive effect is induced by the electromagnetic interaction, this result is in sharp contrast to the textbook knowledge that the ratio of the gravitational force to the electromagnetic force is $Gm_em_p/e^2=4.4\times10^{-40}$ in a hydrogen atom. With unrealistically large values of parameters, we illustrate the two effects on the light trajectories and the intensity map.