Image of a wormhole with an arbitrary throat profile

TL;DR

This paper analyzes the observable signatures of static, spherically symmetric wormholes with arbitrary throat profiles, comparing their shadows and accretion disk images to those of Schwarzschild black holes.

Contribution

It derives general expressions for shadow and silhouette radii for such wormholes and explores how their observable images differ from black holes based on specific parameters.

Findings

Wormhole shadows can match black hole shadows for certain parameters.

Accretion disk images of wormholes are brighter due to Doppler effects.

Differences in images are significant despite similar shadow sizes.

Abstract

We investigate the observable signatures -- the shadow, the throat silhouette, and the image of a thin accretion disk -- for a family of static, spherically symmetric wormholes with an arbitrary throat profile. First, we derive expressions for the shadow radius, the throat silhouette radius, and the photon energy shift for a general static, spherically symmetric metric. Then we apply these results to a specific wormhole metric containing three free parameters: the throat radius~$a$, the throat length~$\lambda$, and the parameter~$u_0$ that controls the depth of the gravitational well. We numerically obtain the shadow and silhouette radii as functions of $\lambda$, $u_0$, and $a$, construct accretion disk images for three representative parameter sets, and compare the results with those for a Schwarzschild black hole. We find that there exist sets of parameters $a$, $\lambda$, $u_0$ such that the wormhole shadow and throat silhouette radii coincide with the shadow and event horizon silhouette of a Schwarzschild black hole of the same mass. Nevertheless, the accretion disk images of these objects differ substantially. In wormhole images, the Doppler effect plays a major role, not the gravitational redshift. As a result, the accreting wormhole images appear brighter.