Explorations Of Two Theoretical Problems In Black Hole Thermodynamics

Black hole thermodynamics is one of the important research directions in modern physics.It combines thermodynamics,classical gravity,and quantum mechanics,and provides a way for the study of quantum gravity theory.Black hole thermodynamics has achieved great successes,and currently an important topic is the black hole thermody-namics in the extended phase space.The extended phase space requires the cosmological constant to be regarded as a dynamic variable,and it has remarkable advantages in describing the similarities between the small-large black hole phase transition and the gas-liquid phase transition of the van der Waals fluid.In addition to the similarities,a black hole may exhibit completely different thermodynamic behaviors from those of the van der Waals fluid,such as the throttling process.The throttling processes of some simple special black holes have been studied,but the most general 4-dimensional rotating and charged black hole solution[Kerr-Newman-anti-de Sitter(KN-AdS)black hole]has not been investigated.In this thesis,we explain the difficulties in the study of the KN-AdS black hole and then systematically investigate the throttling process of the KN-AdS black holes by using a new calculation method.Meanwhile,the inversion temperatures,inversion curves,and isenthalpic curves of the throttling process are studied by both analytical and numerical methods.It is found that the throttling process of the KN-AdS black holes is still similar to those of other simple black holes in many ways,and the differences are also investigated in detail.We also point out and study two special isenthalpic curves:the isenthalpic curve that does not intersect with the inversion curve and the isenthalpic curve that intersects with other isenthalpic curves.Finally,we give a complete description of the throttling process of the most general 4-dimensional black hole.Another research direction of the black hole thermodynamics is the relationship between space-time geometry and thermodynamics.Penrose conjecture suggests that there may be some latent relationship between the Weyl tensor C???? and the entropy of gravitational field.A lot of explorations have been made on the Penrose conjecture,one of which is to construct the Weyl scalar invariant C???? P????,and to calculate the Bekenstein-Hawking entropy of black hole by its volume integral.This idea has been implemented in 5-dimensional Schwarzschild black hole and Schwarzschild-AdS black hole,but it still needs further generalization and verification.In this thesis,we study this idea in more complicated cases,i.e.,the black hole solu-tion with non-spherical horizon—the black ring solution.A black ring is an asymptotically flat vacuum solution of the n-dimensional Einstein equations with an event horizon of topology S1×Sn-3.In the case of 5-dimensional neutral thin black ring,we derive the Bekenstein-Hawking entropy by the volume integral of its Weyl scalar invariant,which verifies the feasibility of interpreting the Weyl scalar invariant as the entropy density of gravitational field in a more general sense.We also calculate several other more compli-cated cases:the black string,the black ring with two angular momenta,and the black ring with a cosmological constant.Although the quantitative results of these cases are somewhat different,they still support our interpretation above.