Photon orbits and phase transitions in Born-Infeld-dilaton black holes

TL;DR

This paper investigates how photon orbit characteristics relate to phase transitions in Born-Infeld-dilaton-AdS black holes, revealing that orbit parameters can serve as indicators of various thermodynamic phase changes.

Contribution

It demonstrates that photon orbit radii and impact parameters signal different black hole phase transitions, establishing their potential as order parameters.

Findings

Photon orbit radius and impact parameter exhibit non-monotonic behavior during phase transitions.

Critical exponents for changes in photon orbit parameters are universally 1/2.

Photon orbit parameters can serve as order parameters for black hole phase transitions.

Abstract

Relations between photon orbits and thermodynamical phase transitions are explored in Born-Infeld-dilaton-AdS black hole. The coupling between the electromagnetic field and the dialton field is chosen such that the full phase diagram contains zeroth-order and first-order phase transitions as well as RPT. We find that there exist non-monotonic beahviors of the photon orbit radius $r_{ps}$ and the minimum impact parameter $u_{ps}$ which signal the existence of the various phase transitions. In particular, the marginal value of pressure under which RPT occur can be read off from these behaviors. Along the co-existing lines, there are changes of both $r_{ps}$ and $u_{ps}$, whose dependence on the transition temperature show characteristic behaviors signalling the existence of RPT. Moreover, the critical exponents of $\Delta r_{ps}$ and $\Delta u_{ps}$ are found to take a universal value $\frac{1}{2}$. These results imply that $r_{ps}$ and $u_{ps}$ can be used as order parameters to describe BH phase transitions.