Null Geodesics and Thermodynamic Phase Transition of Four-Dimensional Gauss-Bonnet AdS Black Hole

TL;DR

This paper explores how null geodesics around a four-dimensional Einstein-Maxwell-Gauss-Bonnet AdS black hole reveal thermodynamic phase transitions, linking gravitational and thermodynamic properties through photon orbit behavior.

Contribution

It introduces a novel approach to study black hole phase transitions by analyzing null geodesics in a modified gravity context, connecting gravitational dynamics with thermodynamic critical phenomena.

Findings

Photon orbit radius varies with phase transition

Minimum impact parameter signals critical behavior

Geodesic behavior reflects thermodynamic phase structure

Abstract

Modified gravity theories are of great interest in both observational and theoretical studies. In this article we study the correlation between the null geodesics in the background of a four-dimensional Einstein-Maxwell-Gauss-Bonnet AdS black hole, a modification of Einstein gravity, and it's thermodynamic phase transition. We study the phase structure of the black hole, using the coexistence and spinodal curves, to understand the phase transition in a extended phase space. The imprints of this phase transition features are observed in the behaviour of photon orbit radius and minimum impact parameter with respect to the Hawking temperature and pressure. The change in these two quantities during the phase transition serve as order parameter which characterises the critical behaviour. The correlation shows that thermodynamic phase transition can be studied by observing the effects of strong gravitational field and vice versa.