Test Of The Weak Cosmic Censorship Conjecture And A Covariant Model For The Energy-momentum Transfer Between DE And CDM

It has been almost half a century since cosmic censorship was proposed by Penrose in1969.Cosmic censorship is still one of the most important open questions in classical general relativity.According to the well-known “Cosmic Censorship Conjecture(WCCC)” first proposed by Penrose,all physical singularities due to gravitational collapse are hidden behind an event horizon.Cosmic Censorship Conjecture implies that no naked singularity occurs in our universe.Determining the validity of cosmic censorship is perhaps one of the most outstanding problems in the study of general relativity.One way of testing the Weak Cosmic Censorship Conjecture is to throw a test particle into an existing black hole.If the particle can pass through the horizon and change the parameters of the black hole such that the horizon disappears,then the cosmic censorship conjecture might break down.The seminal work was done by Wald in 1974.By neglecting the self-force and radiative effects,Wald investigated if a test particle could destroy the event horizon of an extremal Kerr-Newman black hole.In this thesis,one of focus is to investigate the violation of the WCCC by using this test particle approximation method.On the one hand,it is believed that when we have a reasonable and complete quantum theory of gravity available,all spacetime singularities,whether naked or those hidden inside black holes,will be resolved away.As of now,it remains an open question if the quantum gravity will remove naked singularities.On the other hand,we are convinced by the increasing observations that the present universe is dominated by the so called dark energy(DE)and cold dark matter(CDM).Dark energy and dark matter have been two of the very important issues in the Research of cosmology.Some people believe that when we have a complete quantum theory of gravity available,we can also solve the problem of the dark energy and dark matter.In this thesis,our research also involves dark energy and cold dark matter interactions.We suggest a new covariant model for the energy-momentum transfer between dark energy and cold dark matter to avoid the instabilities caused by the evolution of density perturbations on the supper-Hubble scale.In this thesis,beginning with the discussion on the spacetime singularities,we talk about the difference between the curvature singularity and the coordinate singularity.Then we discuss a gravitational collapse may lead to two different collapse end states: black hole,naked singularity.Then we introduce the singularity theorems and cosmic censorship conjecture.Finally,we introduce some elements of standard cosmology in a more quantitative sense.Then we introduce cosmological perturbation theory in the metric approach.In chapter 2,we introduce a gedanken experiment proposed by Wald in 1974.This gedanken experiment is a way of testing the weak cosmic censorship.In chapter 3,we follow the spirit of Wald’s gedanken experiment and further discuss whether a Peldan(MTZ)black hole can turn into a naked singularity when it captures charged and spinning massive particle.We find that feeding a test particle into an extremal or near extremal Peldan(MTZ)black hole could lead to a violation of cosmic censorship for the black hole.We find the allowed energy window is narrow,which indicates that the allowed energy window must be finely tuned.We use the effective potential of a test particle outside the event horizon to show that the particle could easily fall into the black hole.In chapter 4,using the same method,we find that feeding a test particle into an extremal or near-extremal Kerr-Newman-Ad S black hole could lead to destroy their event horizon,giving rise to naked singularities.The allowed energy window is also very narrow.The fact that ?E is very small leaves the possibility of radiative and self-force effects considerations to cure the problem of WCCC violation in Kerr-Newman-Ad S spacetime.Finally,we use the effective potential of a test particle outside the event horizon to show that the particle could easily fall into an extremal or near-extremal Kerr-Newman-Ad S black hole.In chapter 5,we suggest a new covariant model for the energy-momentum transfer between DE and CDM.Using the covariant model,we analyze the evolution of density perturbations on the supper-Hubble scale.We find that the instabilities can be avoided in the model with constant wdand interaction proportional to ρm.Furthermore,we analyze the dominant non-adiabatic mode in the radiation era and find that the mode grows regularly.In chapter 6,we give a conclusion and outlook.