Late-time Tail Of Dirac Particles Around The Rotating Black Hole

One of the two exciting predictions in Einstein's general relativity is that there exists a black hole which is formed from the massive collapsing star. The other is the presence of the singularity, where the modern physics is invalid and the spacetime begins or ends. The black hole has this singularity. Indeed, the analysis of black hole has a significance going far beyond astrophysics, and the black hole physics has become an intersectional field of general relativity, quantum mechanics, string theory, particle physics, thermodynamics and statistics. However, there are still many open questions to be addressed, such as the statistical origin of black hole entropy, the stability of black hole, and the information puzzle. The late-time tail in the black hole perturbation theory is associated with the no-hair theorem, the mass-inflation scenario and the stability of the Cauchy horizon. Therefore it is interesting to investigate this topic.In this thesis, we focus our attention on the late-time tails of the massive Dirac particles around the slowly rotating black hole, while both the observer and the initial data are situated far away from the black hole. The Dirac equations in the curve spacetime are decoupled and separated into the radial and angular parts by using the Newman-Penrose formalism, and then we use the black hole Green's function with the spectral decomposition method to analyze the late-time behavior. Our main conclusions are as follow:1. The intermediate late-time tails of massive Dirac particles in the Kerr spacetime depend not only on the multiple number l and m, the particle massμand spin weight s, but also on the black hole parameter: (a) For mλ＞0, the larger the parameter a is, the more slowly it decays; for mλ＜0, the larger the parameter a is, the more quickly it decays. (b) Forλ＞0, with the same multiple number l, m decrease the decay rate; and forλ＜0 case, m increase it.2. The intermediate late-time tails of massive Dirac particles in the KerrNewman spacetime are studied:(a) The dumping exponent depends not only on the angular quantum number l and m, but also on the product seQ of the spin weight of the Dirac field and the charges of the black hole and the fields, seQ＜0 speeds up the decay but seQ＞0 slows it down.(b) For both positive and negative electric charge Q, the rotating parameter a slows the decay rate down for mλ＞0 but speeds it up for mλ＜0.3. The decay rate of the asymptotically late-time tails of massive Dirac fields in Kerr-Newmem spacetime is t^-5/6 sin(μt), which may be a general feature for late-time tails of massive fields in the 4-dimensional black hole background.4. Compared with the massive scaler fields, the massive Dirac particles in the rotating background have completely different intermediate late-time tails:(a) The intermediate late-time behavior of massive Dirac particles is dominated by a decaying tail without any oscillation, which is different from the oscillatory decaying tail of the scalar fields.(b) The intermediate late-time tails of massive Dirac particles are slower them those of the massive scalar fields.