| Black holes are the most extreme compact object that have been confirmed to exist in the universe.The study of black holes has always been the focus of gravitational theory research,especially their thermodynamic properties.In recent years,with the successful direct observation of the gravitational wave and the shadow of the black hole,it has become a new hot topic to connect the thermodynamics and phase transition of the black hole with the observable gravitational effect.The relationship between the photon orbit and the phase transition of the charged AdS black hole has already been studied.This article mainly extends the study to the Born-Infeld-AdS black hole and explores whether the interesting novel phase transition of the Born-Infeld-AdS black hole—reentrant phase transition—can be revealed by photon orbit in four and higher space-time dimensions.This research can provide direction for the future study of relationship between more abundant types of phase transition and photon orbit,as well as the observation by Event Horizon Telescope.We first discussed the Born-Infeld-AdS black hole metrics and calculated the basic thermodynamic parameters and equation of state of this black hole based on previous studies.Then,according to the difference in the number of thermodynamic critical points caused by different Born-Infeld parameters b,we can divide Born-Infeld-AdS black hole system into four cases.Type I does not have any phase transition,and types II and III have a reentrant phase transition,but one of the two critical points of type III has a negative pressure,and type IV only has a van der Waals-like phase transition.For these different cases,we obtain the corresponding pressure-temperature phase structures and temperaturespecific volume diagrams.The tiny differences between these cases are clearly displayed.Then,we calculate the radius rpsand the minimal impact parameter upsof the photon sphere via the effective potential of the radial motion of photons.rpsand upsare found to have different behaviors in the different cases.Especially,when there is a reentrant phase transition,the temperature exhibits a decrease-increase-decrease-increase behavior for fixed pressure with the increase of rpsor ups,while the pressure exhibits an increase-decrease-increase-decrease behavior instead for fixed temperature.These behaviors are quite different from that of the van der Waals-like phase transition.Near the critical point,the behavior of rpsand upsfor the black hole phase transitions confirms a universal critical exponent of 1/2.We also find that the temperature and pressure corresponding to the extremal points of rpsand upsare highly consistent with the thermodynamic metastable curve for black hole systems with different values of b.Furthermore,because the thermodynamic properties in the high-dimensional Born-Infeld-AdS black hole are very different from the four-dimensional case,we have extended the corresponding research to the high-dimensional black hole.We calculated the equations of the photon orbit radius and minimum impact parameters of the high-dimensional Born-Infeld-AdS black hole.Then we draw the curve of the temperature changes with rpsand ups under the fixed pressure in 5-8 dimensional space-time.We found that when the pressure is lower than the critical pressure,the temperature exhibits "increasing-decreasing-increasing" behavior with the increase of the photon orbital parameters,which is consistent with the conclusion that only van der Waals-like phase transitions exist in high-dimensional black holes.By calculating the critical exponent,we prove that even in high-dimensional space-time,the Born-Infeld-AdS black hole still satisfies the universal critical exponent 1/2.The results show that the photon sphere behaves quite differently for the van der Waals-like and reentrant phase transitions,and both phase transitions can be identified via the photon sphere.And this conclusion is also valid for high-dimensional BornInfeld-AdS black holes... |
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