Violation of Hod's Conjecture and Probing it with Optical properties of a 5-D black hole in Einstein Gauss-Bonnet Bumblebee theory of gravity

TL;DR

This paper investigates the quasinormal modes and optical properties of a 5-D black hole in Einstein Gauss-Bonnet Bumblebee gravity, revealing conditions under which Hod's conjecture is violated or upheld.

Contribution

It introduces analysis of Hod's conjecture in a 5-D Einstein Gauss-Bonnet Bumblebee black hole, highlighting the effects of Lorentz symmetry breaking and Gauss-Bonnet coupling.

Findings

Lorentz symmetry breaking favors Hod's conjecture

Higher Gauss-Bonnet coupling increases violation chances

Lower black hole lifetime supports Hod's conjecture

Abstract

In this work, the quasinormal modes of a $5$-D black hole in Einstein Gauss-Bonnet Bumblebee theory of gravity have been investigated with the help of the Pad\'e averaged higher order WKB approximation method and the validity of Hod's conjecture has been studied. It is found that the presence of Lorentz symmetry breaking due to the Bumblebee field favours Hod's conjecture. But in the case of the Gauss-Bonnet term, an increase in the coupling parameter increases the chances of violation of Hod's conjecture. We further investigated the optical properties of the black hole {\it viz.}, shadow and emission rate. It is found that a black hole with a lower lifetime favours Hod's conjecture.