The Thermodynamic Solution Of Einstein's Field Equations And The Study Of Global Unipolar Space-time

Since Beckenstein proposed the black hole thermodynamics,the researchers has focused on the insightful relationship between gravity and thermodynamics for a long time.In 1975,by applying the quantum field in curved spacetime,Hawking claimed that the black hole could be viewed as a thermodynamical system exactly,and the radiation is the well known black body's radiation indeed.In,1995,Jacobson derived the Einstein equations from the thermodynamical laws basing on the local equilibrium assumption.In 2014,a paper pub-lished in Physical Review D derived several exact solutions of Einstein equations from the thermodynamical laws without out applying such equations.However,in such work,the authors applied the Misner-Sharp(MS)energy as the energy of gravitational field,indi-cating that there method only works in very special situations,for the MS eneergy can only be defined in the spacetime with the maximal symmetries.Thus,one work of this thesis is trying to generalize such method.In 1989,Harari and Lousto first proposed the global monopole spacetime.However,such work is basing on the weak field approximation.Therefore,our another work is trying to derive such spacetime exactly.There are mainly two aspects of work in this thesis.Firstly,we modify the method that generates the exact solutions of Einstein equations from thermodynamical laws.In our method,we replace the Misner-Sharp(MS)energy with both the Komar mass and the ADM mass.Besides,we claim that the global monopole spacetime is an exact solution of Einstein equations,and the matter field of such spacetime is the nonlinear ? model indeed.Further-more,we reconstruct the definition of the so call topological charge in a more convincing way.In the introduction of this thesis,we give a brief review of the history of the black hole thermodynamics.Plus,we review the the method that generates the global monopole spacetime in an approximated way as well as the original construction of the topological charge.In chapter 2,we present how to modify the method which generates the exact solutions of Einstein equations from thermodynamical laws.Firstly,we replace the MS energy with only the Komar mass.Basing on some rational assumptions,we obtain several exact solutions of Einstein equations.Furthermore,we use both the Komar mass and the ADM mass to complete such modification.Besides,we generalize the definition of the ADM mass in the spacetime with the global monopole charge,and then we present some discussions of such spacetime.In chapter 3,we claim that the global monopole space time is an exact solution of Einstein equations,and the matter field of such spacetime is the nonlinear ? model,and then we construct the definition of the topological charge in a more convincing way.We also find the general expression of the action of the matter field which could be used to generate such spacetime.In addition,we generalize our discussions to higher dimensional aspcetime as well as the plane-symmetric spacetime and the hyperbolically-symmetric spacetime.We also investigate the thermodynamical properties of the global monopole spacctime and the topological charge.Finally,we give a brief summary and discussion of the work of this thesis in the last chapter.There are also some overlooks of future research in that chapter.