4-charge Static (AdS Or Squashed) Black Holes In Five-dimensional N=2 Supergravity

Black holes are the most fundamental and important objects predicted by Einstein's General Relativity.The construction of exact solutions of black holes and studying their properties can help us deepen our understanding of the nature of(super-)gravities and the basic properties of space-times.Due to various kinds of exotic properties of black holes in higher dimensions and supergravity theories different from their fourdimensional counterparts,they attracted a lot of attentions in recent years.The topics of this thesis are our new researches about 4-charge static solutions of(AdS or squashed)black holes in five-dimensional N=2 supergravity and their thermodynamic properties.As far as the five-dimensional N=2 supergravity theory is concerned,its bosonic part can,in general,contain n vector supermultiplets in addition to the graviton and graviphoton.The most famous solutions in this theory are those found in n=2 U(1)3 supergravity theory(namely,five-dimensional N=2 supergravity coupled with 2 Abelian vector supermultiplets),also named as the STU model.In the past two decades,a lot of researches have been done within this STU model and many meaningful solutions of black holes and black rings have been obtained.It can be conjectured that some unknown black hole solutions might still exist in the general theory of five-dimensional N=2 supergravity.Although there has been much progress in obtaining a large amount of new black hole solutions of five-dimensional N=2 supergravity theory over the past few years,almost all of them are limited to the STU model,namely,those black hole solutions with three charges.Little has been done in the n>2 case.In this thesis,we shall consider the n=3 ungauged supergravity theory,namely,five-dimensional N=2 supergravity coupled with 3 Abelian vector supermultiplets,which will be dubbed as“STU-W2U”model.We have made some deeper investigations of the nonextremal black hole solutions within this model and now have constructed some new 4-charge static solutions of black holes and its Kaluza-Klein(KK)squashed counterparts in the five-dimensional ungauged supergravity theory as well as its static AdS generalizations in gauged supergravity.The main content of this work is to construct new 4-charge black hole solutions in the five-dimensional N=2 supergravity and to study their thermodynamic properties.First of all,we shall present the 4-charge static black hole solution and its KK version with squashed horizons in this theory,and then obtain the 4-charge static AdS black hole solution in gauged supergravity.In the meanwhile,we will investigate extensively their thermodynamic properties.The structure of this thesis is divided into six chapters.In the first chapter,after a brief introduction to General Relativity,black hole physics,superstring theory,supergravity,higher dimensional space-time,exact solutions in five dimensions and the thermodynamic properties of black holes,we present the background acknowledge underlying our researches and its significance of the subjects.In the second chapter,we first briefly introduce five-dimensional N=2(gauged)supergravity theory.Then using the simplest but most representative STU model as an example,we present in detail the solving procedure of the static five-dimensional three-charged AdS black hole solution.The third to the fifth chapters are the focus of this thesis and constitute completely new and original work.In the third chapter,we first give the bosonic action of the STU-W2 U model in five-dimensional N=2 supergravity and derive all equations of motion.Next,we present a new solution for the five-dimensional static black hole with four independent charges and calculate its thermodynamic quantities by verifying that they perfectly obey the first law of black hole thermodynamics.In the fourth chapter,we will generalize our 4-charge static solution obtained in the STU-W2 U model to the case with a negative cosmological constant(namely,in AdS space-time).We obtain the 4-charge static AdS black hole in gauged supergravity and then analyze its thermodynamic properties in detail.In the fifth chapter,we will further generalize our 4-charge static black hole solution to that with squashed horizons and present its explicit expression of 4-charge static squashed black hole in supergravity,followed by the analysis of its thermodynamic properties.The sixth chapter is a brief summary of this thesis and the outlook for the follow-up work.