Thermodynamic Phase Transition Of Black Holes And Its Relations To Photon Orbits

Black hole thermodynamics is an innovative hot topic in current gravitational theory and black hole physics.Especially in the Ad S/CFT framework,black hole thermodynamics in Ad S spacetime background has attracted great attention.In this context,considering the cosmological constant as the thermodynamic pressure and interpreting the inner energy as the enthalpy of the BH system,black hole thermodynamics completely agrees with that of ordinary thermodynamic systems,and thus the four laws of black hole thermodynamics have also been greatly improved.In the phase space,Hawking and Page firstly discovered the so-called Hawking-Page phase transition,that is a transition between the Schwarzschild-Ads black hole and the thermal Ad S space.After that the vd Ws-like phase transition between large and small black holes and reentrant phase transition have also been found in charged or rotating Ad S black holes respectively,which have been given a heuristic explanation from the aspects of thermodynamic geometry,string theory and statistical mechanics etc.These studies play a key role in the understanding of black hole microstructure and the construction of quantum gravity theory.In this thesis,we first study the rich phase structures of Born-Infeld-dilaton-Ad S black hole which may contain zeroth-order,first-order as well as reentrant phase transition(RPT)depending on the value of the coupling constant α between the electromagnetic field and the dilaton.We try to give a microscopic explanation for these phase transitions by adopting Ruppeiner’s approach.By studying the behaviors of the Ruppeiner invariant R along the co-existing lines,we find that the various phase transitions may be qualitatively well explained as a result of two competing factors: the first one is the low-temperature effect which tends to shrink the BH and the second one is the repulsive interaction between the BH molecules which,on the contrary,tends to expand the BH.In the standard phase transition without RPT,as temperature is lowered,the first kind of factor dominates over the second one,so that large black hole(LBH)tends to shrink and thus transits to small black hole(SBH);While in the RPT,after the LBH-SBH transition,as temperature is further decreased,the strength of the second factor increases quickly and finally becomes strong enough to dominate over the first factor,so that SBH tends to expand to release the high repulsion and thus transits back to LBH.Moreover,by comparing the behavior of R versus the temperature T with fixed pressure to that of ordinary two-dimensional thermodynamical systems but with fixed specific volume,it is interesting to see that SBH behaves like a Fermionic gas system in cases with RPT,while it behaves oppositely to an anyon system in cases without RPT.And in all cases,LBH behaves like a nearly ideal gas system.Then we explore the relations between photon orbits and thermodynamical phase transitions in Born-Infeld-dilaton-Ad S black hole.We find that there exist non-monotonic beahviors of the photon orbit radius and the minimum impact parameter as the temperature decreases,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 orbits radius and impact parameter,whose dependence on the transition temperature show characteristic behaviors signalling the existence of RPT.Moreover,we found through numerical fitting that the critical exponents of the difference,before and after the phase transition,in photon orbits radius and the minimum impactparameter are found to take a universal value 1/2 obtained by other ways.Theseresults imply that photon orbits radius and the minimum impact parameter can be used as order parameters to describe BH phase transitions.