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

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 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 occurs can be read off from these behaviours. Along the co-existing lines, there are changes of both r(ps) and u(ps), whose dependence on the transition temperature show characteristic behaviours signalling the existence of RPT. Moreover, the critical exponents of Delta r(ps) and Delta u(ps) are found to take a universal value 1/2. These results imply that r(ps) and u(ps) can be used as order parameters to describe BH phase transitions. (C) 2020 The Authors. Published by Elsevier B.V.