Constraints on the $\gamma$-parameter for the vacuum solution of Cotton gravity with geodesics and shadows

TL;DR

This paper constrains the $oldsymbol{ ext{γ}}$-parameter in Cotton gravity using Event Horizon Telescope data of Sgr A*, analyzing geodesics and shadows to assess observational distinguishability from general relativity.

Contribution

It provides the first observational constraint on the $oldsymbol{ ext{γ}}$-parameter in Cotton gravity based on supermassive black hole imaging data.

Findings

The $oldsymbol{ ext{γ}}$-parameter is constrained to $oldsymbol{ ext{γ} M oughly 3.5 imes 10^{-12}}$ at 2σ.

Current observational techniques cannot distinguish Cotton gravity from General Relativity.

The smallness of $oldsymbol{ ext{γ}}$ limits observable deviations in photon rings and shadows.

Abstract

We consider a recently introduced extension of General Relativity dubbed as Cotton gravity (CG), based on the use of the Cotton tensor, to estimate the size of a new constant $\gamma$ appearing within a spherically symmetric, vacuum solution of the theory. Taking into account its non-asymptotically flat character, we use the inferred size of the central brightness depression of the supermassive object at the heart of the Milky Way galaxy (Sgr A*) by the Event Horizon Telescope to constrain at $2\sigma$ the CG parameter as $\gamma M \approx 3.5 \times 10^{-12}$. We study the potential observational consequences from the smallness of such a value using exact and numerical expressions for the deflection angle, optical images from optically and geometrically thin accretion disks, isoradials, and instability scales (Lyapunov index) of nearly bound geodesics associated to photon rings. Our results point towards the impossibility to distinguish between these two geometries using current and foreseeable techniques in the field of interferometric detection of optical sources.