Black Hole Shadows Constrain Extended Gravity

TL;DR

This paper develops a method to analyze black hole shadows in extended gravity theories, comparing predictions with Event Horizon Telescope data to constrain various models without considering black hole rotation.

Contribution

It introduces a shadow background calculation method for non-rotating black holes in extended gravity theories, extending previous models and applying it to observational data.

Findings

Horndesky model with Gauss-Bonnet invariant agrees with M87* observations

Large parameters in conformal gravity are excluded by data

Constraints on $f(Q)$ gravity and Bumblebee model parameters are established

Abstract

The first images of black hole shadows open new possibilities to constrain modern extended gravity theories. We present the method of shadow background calculation for black hole solutions in the form of Taylor series where $g_{11} = - g_{00}^{-1}$. The method is extended to general non-rotating case $g_{11} \neq - g_{00}^{-1}$. The results of the analysis are compared with the predictions of General relativity taking into account the Event Horizon Telescope data. The results for the Horndesky model with the Gauss-Bonnet invariant, loop quantum gravity, Bumblebee model and Gauss-Bonnet gravity are in full agreement with the observations of M87*. In conformal gravity, large values of $m_2$ and $Q_s$ must be excluded. In STEGR $f(Q)$ gravity the observational limits on the parameter $\alpha$ are: $-0.025<\alpha<0.04$. For an alternative generalization of the Bumblebee model with the Schwarzschild approximation: $-0.3 < l < 0.45$. These results demonstrate the maximum one can achieve without taking into account of the rotation of a black hole.