Shadows and thin accretion disk images of the $\gamma$-metric

TL;DR

This paper investigates the shadows and accretion disk images of the $b$-metric, a vacuum solution without an event horizon, to understand its observational signatures and compare them with black holes.

Contribution

It provides the first analysis of shadows and accretion disk images for the $3b$-metric, revealing conditions under which they resemble or differ from black hole images.

Findings

Shadows are absent for $3b < 1/2$.

Shadows for $3b 3ff; 1/2$ are consistent with M87* observations.

Light rings in the $3b$-metric can mimic Schwarzschild black holes.

Abstract

The $\gamma$-metric is a static, axially-symmetric singular solution of the vacuum Einstein's equations without an event horizon. This is a two-parameter family of solutions, generic values of one of which (called $\gamma$) measure the deviation from spherical symmetry. Here, we first study the shadow cast by this geometry, in order to constrain the $\gamma$-metric from observations. We find that for $\gamma < 1/2$, there are, in principle, no shadows cast. On the other hand, shadows cast for all values of $\gamma \geq 1/2$ are consistent with observations of M$87^*$ by the Event Horizon Telescope. We also study images of thin accretion disks in the $\gamma$-metric background. In situations where the $\gamma$-metric possesses light rings, these qualitatively mimic Schwarzschild black holes with the same ADM mass, while in the absence of such rings, they are drastically different from the black hole case.