Black Hole Thermodynamics And The Related Phenomenology

Black hole is not only a special object predicted by General Relativity but also an elegant solution of Einstein equation.The studies on black hole have always been hot in physics and astrophysics for a long time.Quantum gravity combines the principles of general relativity and quantum theory,which expected to be able to provide a satisfactory description of the microstructure of spacetime on the Planck scale.Black hole thermodynamics is one of the candidates to quantum gravity.After considering the quantum effect and the discovery of Hawking radiation in the 1970s,black holes serve as a gravitational dynamic system,the formation of black holes' quantities are similar to those in daily thermodynamic system,then the four laws of thermodynamics of black hole have been proposed.Afterwards,physicists have been widely exploring black hole thermodynamics to understand the nature of the black hole.Later,researchers proposed to treat cosmological constant as the pressure of black hole thermal system,and its conjugation is the thermodynamic volume.By introducing pressure and volume into black hole thermal system,one has the extended thermodynamics of black hole which is the so-called black hole chemistry,in which the mass of black hole is enthalpy rather than the internal energy of black hole.Subsequently,abundant phase structure and thermodynamic behavior can be obtained in such a special thermal system.Black holes exhibit similar behavior of Van de-Waals fluid and various phenomena have been investigated such as pressure-volume phase transition,triple points and reentrant transition.In this thesis,we first review the history of black hole and their features,especially for the black hole thermodynamics.Then we focus our study on their phenomena of thermodynamics behavior in the extended phase space,such as holographic heat engine and Joule-Thomson effect.This thesis is divided into two main parts.In the first part we study the Smarr relation which is related to the first law of black hole thermodynamics,and then we investigate the validity of the thermodynamic laws when black hole has energy exchange with the outside system.In the second part,we investigate the phenomena in the extended thermodynamic of black hole,such as holographic heat engine and Joule-Thomson effect.In details,this thesis is organized as follows:In chapter 1,we review the definition of black hole,its research history and the thermodynamics of black hole,especially the extended thermodynamics of black hole in which a dynamical cosmological constant is presented as pressure.In chapter 2,we describe what is the Smarr relation and how to derive it.The usual method to get Smarr relation is via scaling analysis.However,in the extended phase space,it is not necessary in Horndeski gravity with the k-essence sector.We discuss this issue about the Smarr relation when involving dimensional coupling constants.In chapter 3,we study the variation of AdS black hole in the extended phase space when charged particle falling into black hole.Recently,a series of studies addressed that the second law of black hole violates after charged particle absorbed by black hole.We revisit this violation of second law via two different methods here.The first is to redefine the energy of black hole changed by the falling particle,we argue that the possible reason for the violation of the second law may contribute to the wrong assumption that the change of the internal energy of the black hole is equal to the energy of the particle.Then we show the variation of massive black hole in both extended and normal phase spaces.The thermodynamics under particle absorbing and the weak cosmic censorship are studied.We reclaim the violation of the second law comes from the wrong assumption which needs to be carefully treated.In chapter 4,the holographic heat engine with momentum dissipation was introduced.We first review the exact black hole solution in Horndeski gravity with k-essence sector and its thermodynamics.Then we define a holographic heat engine in this model and estimate the engine efficiency with high temperature limits.The coupling constants' effects on efficiency and the comparison with Carnot efficiency are studied in this chapter too.In chapter 5,we investigate the Joule-Thomson effect in the AdS black hole.We consider Joule-Thomson effect in Einstein-Maxwell gravity and Massive gravity in which the translational invariance is broken via two different mechanisms.As a first attempt,we obtain the Van der-Waals like behavior in black hole system,which enrich the phenomenal analysis in the extended thermodynamic of black holes.Chapter 6 contributes to our discussions and conclusions.