Entropies And Singularities Of Black Holes

The properties of black hole thermodynamics and the singularities are two important issues of black holes.This dissertation focuses on the entropy of black holes in the black hole thermodynamics.Till now,we don't have unified conclusion about the origin of the black hole entropy.Different thinking of the origin corresponds to different models.By using the popular models named brick-wall model and membrane model,this dissertation discusses the origin of the black hole entropy,where the membrane model is the modified brick-wall model.However,there are some shortages of the two models.Both the two models need a man-made cut-off in order to satisfy the result of Bekenstein-Hawking entropy.Beside this,the semi-classical condition in membrane model might be invalid.The two problems are tried to be solved in chapter two.In section 2.2,by introducing the GUP(generalized uncertainty principle),the dissertation modified the membrane model,and calculated the static Schwarzschild-de Sitter black hole and non-static Vaidya black hole.During the calculations,the man-made cut-offs are naturally removed and turn into the natural cut-offs.The natural cut-offs are determined by the black holes themselves and the minimal length.And also give out the proper value of the minimal length.Moreover,in section 2.3,by using the general conclusion of the GUP in other works of black holes,the two parameters are modified,and one could get the connections between the requirements of black holes' mass are the same with the requirements of the existences of black holes.Meanwhile,the requirements also insure the validation of the semi-classical condition and bring physical meanings to the two parameters.In section 2.4,this dissertation considers the entropy of entanglement between different horizons which is ignored before.And get the new total entropy of the black hole.An extra item is added and find the total entropy would be divergent when the horizons close to each other.This is a new result.The singularities are the fundamental prerequisite,it is also an important issue in cosmology.There should be no naked singularities according the WCCC(weak cosmic censorship conjectures),which is still not been proved till now.By throwing a test particle into the black hole,chapter 3 investigate whether the black hole can absorb the test particle and change its mass,charge or angular momentum so that its horizons will disappear,and the naked singularities show out.Or to find some ways to protect the black hole from being destroyed.In section 3.2,a Peldan Electrostatic solution black hole is discussed both on extremal case and near-extremal cases.And find it could be destroyed by some particular particles,and one could see the naked singularities.This is a challenge to WCCC.The probable reason might be the neglect of radiative and self-force effects?The quintessence is considered in section3.3 and find the RN-Q(Reissner-Nordstr?m-Quintessence)black hole could be protected by quintessence item rather than be destroyed like Reissner-Nordstr?m black hole.This result also might be a support to quintessence model in dark energy physics.