Testing EGB gravity coupled to bumblebee field and black hole parameter estimation with EHT observations

TL;DR

This paper explores rotating black holes in a modified gravity theory coupled with a vector field, using EHT observations to estimate black hole parameters and assess the theory's astrophysical viability.

Contribution

It introduces a novel model of Kerr EGB bumblebee black holes and develops a parameter estimation method using EHT data to test this theory against observations.

Findings

KEGBB and Kerr black holes are indistinguishable in some parameter ranges.

EHT observations constrain the parameters of the KEGBB black holes.

The model remains a viable candidate for describing astrophysical black holes.

Abstract

A general covariant Einstein-Gauss-Bonnet Gravity in Four-Dimensional (4D EGB) spacetime is shown to bypass Lovelock's theorem and is free from Ostrogradsky instability. Meanwhile, the bumblebee theory is a vector-tensor theory. It extends the Einstein--Maxwell theory that allows for the spontaneous symmetry breaking that leads to the field acquiring a vacuum expectation value, introducing Lorentz violation into the system. We investigate rotating black holes in the 4D EGB-bumblebee gravity model where Lorentz symmetry is spontaneously broken -- Kerr EGB bumblebee (KEGBB) black holes. The latest observations from the Event Horizon Telescope (EHT) of the supermassive black holes (SMBHs) M87* and Sgr A* have sparked intensified interest in the study of black hole shadows, which present a novel avenue for investigating SMBHs within the strong-field regime. Motivated by this, we model SMBHs M87* and Sgr A* as KEGBB black holes, and using the EHT observation result, for given $l$, to find earlier upper limits on the $\alpha$ and $a$ are altered. The KEGBB and Kerr black holes are indiscernible in some parameter space, and one cannot rule out the possibility that the former may serve as strong candidates for astrophysical black holes. Employing our newly developed parameter estimation technique, we use two EHT observables -- namely, the angular diameter of the shadow, $d_{sh}$, and the axial ratio, $\mathcal{D}_A$ -- to estimate parameters of M87* and Sgr A* taking into account observational errors associated with the EHT results.