Killing Of Black Hole Thermodynamics And The Space-time Is Reduced

The paper gives a summary of the author' s research work in three aspects: (1) discussing the quantum thermal effect of nonstationary black hole; (2) describing the application of the generalized uncertainty relation to the discussion of black hole entropy; (3) studying the reduction of spacetimes with a Killing symmetry. There are five chapters in the paper. Chapter 1 provides a review about the background and theories related to the work of the author. Chapter 2,3,4 summarize the research work of the author. Chapter 5 gives the summarization and prospects of the research work.The first work described in chapter 2 is the research on the quantum thermal effect of a radiating rotating arbitrarily accelerating black hole and a nonstationary Kerr-Newman black hole, whose metrics are changing slowly. First, a radiating rotating arbitrarily accelerating black hole is studied. The concept of local thermal equilibrium is introduced into a nonstationary black hole whose metric is changing slowly; the radiation temperature is obtained which depends on the time and the angles on the horizon and is a local quantity; the Hawking thermal spectrum formula is gained which is a quasi-black-body' s thermal spectrum; The black hole entropy is calculated which is proportional to the horizon area only with a appropriate geometrical cutoff relationship. Alternative cutoff relationships are got through discussion. One of them is very simple and it seems that there is something in common between the nonstationary black hole and a spherical and static black hole due to the same of their cutoff relationships. Another of them is more complicated but more reasonable and consistent with the ones of some known more simple nonstationary black hole and non-spherical black hole, whose cutoff relationships also deviate static and spherically symmetric case. Then, a nonstationary Kerr-Newman black hole is researched. The radiation temperature is calculated which is also a local quantity; the Hawking thermal spectrum formula is obtained which is also a quasi-black-body' s thermal spectrum; The black hole entropy is gained and is proportional to the horizon area with a suitable cutoff relationship. The research on the two nonstationary black holes shows that the improved method of Damour-Ruffini and the thin film modelcan be effectively applied to the study of a complex black hole on the only condition that nonstationary metric is changing slowly.The next work summarized in chapter 3 is the study of how the generalized uncertainty relation influence the calculation of black hole entropy. First, the generalized uncertainty relation and the brick wall model are utilized to investigate Schwarzschild black hole. The conclusion is expounded and proved that we can't obtain the black hole entropy proportional to the horizon area from the expression of entropy when the distance of two brick walls is long enough. So, we can conclude that the brick wall model is ineffectual while the generalized uncertainty relation is applied to the discussion of black hole entropy. Then, the statistical entropies of Klein-Gordon field and Dirac field inside a Planck thin film on the horizon surface are calculated respectively by combining the generalized uncertainty relation with the thin film model. This leads to both removing the cutoff and acquiring a black hole entropy proportional to the horizon area. The work of this chapter testifies further that applying the generalized uncertainty relation to the study of black hole thermodynamics is effective and the thin film model is rational.The final work given in chapter 3 is the investigation on Killing reductions of 4-dimensional and 5-dimensional spacetimes. First, the 3-dimensional action obtained from the Killing reduction of 4-dimensional action is discussed, the variations of which lead to the same field equations as those reduced from the vacuum Einstein equation by Ge-roch; Then, a series of equations parallel to Geroch's are acquired by extending Geroch's approach to a 5-dimensional spacetime with a Killing symmetry, this provides a new version 5-dimensional Kaluza-Klein theory during the spacelike Killing vector field and a vacuum case. Next, the Killing reduction of spacetime is studied from the viewpoint of variation principle. It turns out that the symmetry-reduced 4-dimensional action from the 5-dimensional Hilbert action would give the correct field equations reduced from 5-dimensional vacuum spacetime with a Killing symmetry by variations with respect to a series of suitable field variables. Finally, an alternative special 4-dimensional action is obtained. Its variations with respect to the other series of field variables can also give thesame field equations reduced from 5-dimensional vacuum field equations. The research described in this chapter shows that the final result of " n-dimensional action^=> reduced (n-l)-dimensional action^=> (n-l)-dimensional spacetime field equations obtained by variations " and that of " n-dimensional action^=> n-dimensional spacetime field equations obtained by variations^=> (n-1)-dimensional spacetime field equations obtained by reduction of n-dimensional field equations " are the same and 5-dimensional gravity with a Killing symmetry is equivalent to 4-dimensional gravity coupled to a vector field and a scalar field.