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

Abstract

Relations between photon orbits and thermodynamical phase transitions are explored in Born-Infeld-dilaton-AdS black hole (BH). 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 reentrant phase transition (RPT). We find that there exist non-monotonic beahviors of the photon orbit radius rps and the minimum impact parameter ups which signal the existence of the various phase transitions. In particular, the marginal value of pressure under which RPT occurs can be read off from these behaviours. Along the co-existing lines, there are changes of both rps and ups, whose dependence on the transition temperature show characteristic behaviours signalling the existence of RPT. Moreover, the critical exponents of Δrps and Δups are found to take a universal value 12. These results imply that rps and ups can be used as order parameters to describe BH phase transitions.