Research On The Topic Of The Lagragian Method And Weak Cosmic Cencorship Conjecture

It is well known that the gravitational field equation is the core of the theory of gravity,but because it is a complex second-order partial differential equation system,the equation system itself cannot directly reflect more information unless to solve it,and classical physics tells us that we can use the language of differential geometry to solve physical problems.Valence is transformed into a variational problem on a symplectic manifold.Since this equivalent description can reflect more information than the equation itself,it can often be more general than solving field equations when dealing with certain physical problems.For the study of variational problems,Noether’s theorem plays an important role.Noether’s two major theorems have a wide range of applications in modern physics.They connect symmetry with conservation laws and constraint equations,and they have also received important applications in the development of their gravitational theory.Using Noether’s theorem and the method of variation can extract the general laws that can be given by the system symmetry from the theory of gravity without solving the solution of Einstein’s equation.This generality implies that even we are at the level of action,some conclusions about the theories involved can be extracted.Since Penrose put forward the hypothesis of cosmic censorship,there has been a lack of a general argument for the validity of this hypothesis.The verification of this hypothesis mainly involves the specific solution of Einstein’s equation in previous work.In this paper,we firstly reviewed Noether’s theorem,variational principles,analytical mechanics,and some knowledge of related geometry in detail.By defining several existing conserved quantities of black holes that can be obtained,we define them as linear stretcher black holes.The conclusions below are compared to illustrate the equivalence of several forms.It wanted to show the superiority and naturalness of Lagrangian method developed only from Noether’s theorem and variational principle.Because of this,the variational equation in the theory of gravity can be obtained.And this variational equation has important and broad application prospects.In this article,we only consider using it to conduct a new version of the thought experiment to verify the hypothesis of weak cosmic supervision.but this kind of thinking pattern,based on the reflection of the mathmatical language behind the physics phenomenen,has the potential to be used for solving other questions.