Wave-optical treatment of the shadow cast by a large gravitating sphere

TL;DR

This paper develops a wave-optical model to analyze the shadow of a large gravitating sphere, revealing its shape and properties influenced by spacetime curvature and gravitational effects.

Contribution

It introduces a wave-optical approach with absorbing boundary conditions to accurately model the shadow of a gravitating body in general relativity.

Findings

Shadow shape is a concave hyperboloid influenced by Schwarzschild radius.

No light exists within the shadow region.

Presence of the Arago spot behind the sphere despite gravitational bending.

Abstract

We study the shadow cast by a large gravitating sphere, similar to our Sun. For this, we consider the gravitational field produced by a static mass monopole within the first post-Newtonian approximation of the general theory of relativity. We study the propagation of a monochromatic electromagnetic wave in the vicinity of a large, opaque, gravitating sphere. To treat the opaque nature of the body and its physical size, we implement fully absorbing boundary conditions and develop a wave-optical treatment of the shadow formed by this object. Based on this approach, we demonstrate that the structure of the shadow is determined by the Schwarzschild radius of the body and its physical size. The shadow's boundary has the shape of a concave rotational hyperboloid bent inward due to the refractive properties of the curved spacetime. We show that there is no light in the shadow. However, even in the presence of gravity and related gravitational bending of photon trajectories there is the bright spot of Arago that is formed behind a perfectly spherical obscuration.