Photon sphere and reentrant phase transition of charged Born-Infeld-AdS black holes

Abstract

Comparing to the charged AdS black hole in GR, a new interesting phase transition, the reentrant phase transition, is observed in a charged Born-Infeld-AdS black hole system. It is worth to extend the study of the relationship between the photon sphere and the thermodynamic phase transition, especially the reentrant phase transition, to this black hole background. According to the number of the thermodynamic critical points, the black hole systems are divided into four cases with different values of Born-Infeld parameter b, where the black hole systems can have no phase transition, reentrant phase transition, or Van der Waals-like phase transition. For these different cases, we obtain the corresponding phase structures in pressure-temperature diagram and temperature-specific volume diagram. The tiny differences between these cases are clearly displayed. On the other hand, the radius rps and the minimal impact parameter ups of the photon sphere are calculated via the effective potential of the radial motion of photons. For different cases, rps and ups are found to have different behaviors. In particular, with the increase of rps or ups, the temperature possesses a decreaseincrease-decrease-increase behavior for fixed pressure if there exists the reentrant phase transition.While for fixed temperature, the pressure will show an increase-decrease-increase-decrease behavior instead. These behaviors are quite different from that of the Van der Waals-like phase transition.Near the critical point, the changes of rps and ups among the black hole phase transition confirm an universal critical exponent 1 2 . Finally, we also find that the temperature and pressure corresponding to the extremal points of rps and ups are highly consistent with the thermodynamic metastable curve for the black hole systems with different values of b. Therefore, all the results indicate that, for the charged Born-Infeld-AdS black holes, not only the Van der Waals-like phase transition, but also the reentrant phase transition can be reflected through the photon sphere.

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

“…In particular, these changes have an universal exponent 1 2 near the critical point. Later, the study is extended to other black holes and gravity theories, for example rotating case [51], Gauss-Bonnet case [52], massive gravity case [53] and Born-Infeld case [54], which confirm the relations further. See also Ref.…”

Kinetics of a phase transition for a Kerr-AdS black hole on the free-energy landscape

“…Phase transition for a broad class of asymptotically AdS hairy black holes in Lovelock gravity strongly resembles those of superfluidity in liquid helium [33]. Further investigation reveals that properties of phase transition for asymptotically AdS black holes can be reflected from the quasinormal modes and null geodesics [34][35][36]. For a comprehensive review of black hole thermodynamics and phase transition, see Refs.…”

Can shadows reflect phase structures of black holes?

“…Based on the case studies in [38,39], it was found that the circular orbit radius of the photon can be a characteristic quantity to reflect the thermodynamic phase structure of a spherically symmetric black hole [40]. Related extensions can also be seen in [41,42]. The image of the black hole makes us think about whether it is possible to use the black hole shadow, which is observable, to reflect the thermodynamics of the black hole.…”