Black Hole Thermodynamics And Weak Comic Censorship Conjecture

In order to prevent the singularity from being exposed and the phenomenon of "naked singularity",Penrose proposed the weak cosmic censorship conjecture: there is a cosmic supervisor,which prohibits the appearance of naked singularities.As long as the singularity is wrapped in the horizon,the uncertain information it sends will not escape the black hole,so it will not affect the evolution of the universe.In this paper,we discuss whether weak cosmic censorship conjecture is effective by studying black holes in different dimensions and different spacetime backgrounds.First,we use the Hamilton-Jacobian equation and the Dirac equation to derive the energy-momentum relationship of the particle at the horizon,and use this relationship to verify whether the first law of black hole thermodynamics holds.Secondly,the thermodynamic laws of AdS black holes of massive gravity and the weak cosmic censorship conjecture are studied.The study found that the first law of black hole thermodynamics holds no matter in the normal phase space or in the extended phase space.For the second law of black hole thermodynamics,it holds in the normal phase space,but in the extended phase space,for the extreme AdS black hole of massive gravity,the second law of thermodynamics appears to be violated,but for the non-extreme AdS black hole of massive gravity,The second law of thermodynamics holds.Through inspection,it can be found that as the particles are absorbed by the black hole,the black hole always has a horizon radius,so that the singularity is not exposed,in order to verify whether the weak cosmic censorship conjecture is valid.Studies have shown that in normal phase space,as particles are absorbed by black holes,the state of the function for determining the position of the black hole's horizon is stable,and the change of the function for determining the position of the horizon of the black hole is less than zero,which means the black hole's horizon always exists,and the singularity can be avoided from being exposed,so the weak cosmic censorship conjecture is valid.Different from the normal phase space,for the extreme black hole in the extended phase space,as the particles are absorbed by the extreme black hole,the function determining the position of the event horizon does not change,which makes the structure of the extreme black hole unchanged,so the black hole maintains its initial state.In addition,it is found that in the extended phase space,the structure of non-extreme black holes does not change with the absorption of particles.In summary,the weak cosmic censorship conjecture is valid for both extreme black holes and non-extreme black holes in normal phase space and extended phase space.Dark matter is one of the major issues in current theoretical physics and astrophysics,and it may play an important role in the formation of supermassive black holes.Next,we verify the laws of thermodynamics and the weak cosmic censorship conjecture of the Reissner-Nordst?m-AdS black hole surrounded by dark matter.The results found that the conclusions of the first law of thermodynamics and the weak cosmic censorship conjecture are consistent with the conclusions of AdS black holes under mass gravity,but the existence of dark matter parameters will affect the second law of thermodynamics in the extended phase space.In addition,the above methods are used to verify the thermodynamic laws and weak cosmic censorship conjecture of high-dimensional hairy AdS black holes in normal phase space.The results found that the conclusions obtained are also applicable to the case of high-dimensional black holes,That is to say,for all initial states of black holes,the first and second laws of thermodynamics and the weak cosmic censorship conjecture are all valid in normal phase space.