A Study Of Gravity And Thermodynamics Of Horizons And Quantum Tunneling Method Of Hawking Radiation And Related Research

The relation between gravity and thermodynamics of horizons is one of the most interesting things in theoretical physics. Recently, and more importantly, several features related to horizon thermodynamics were discovered: Einstein equations can be expressed as a form of the first law of thermodynamics on horizons; on the apparent horizon of the Friedmann-Robertson-Walker(FRW) universe, the dynamical equation of spacetime (Friedmann equation) also can be expressed as a form of the so-called unified first law of thermodynamics; the locally defined apparent horizon of the FRW universe also related with Hawking radiation in the view of the Kodama vector.Hawking radiation is a very important phenomenon of black hole physics. Parikh and Wilczek further refined and extended the thought of Keski-Vakkuri and Kraus, the radiation was explained as a tunneling process crossing the barrier of horizon, and in literatures the method is called Parikh-Wilczek tunneling method. In our paper, we further studied the effect of Hawking radiation of the apparent horizon of the dynamical spacetime, the FRW universe, and the thermodynamics of the apparent horizon of the dynamical black hole modes, the Vaidya black hole and the McVittie black hole. We also investigate the relations between the radiations and thermodynamics on horizons.Firstly, in the background of the dynamical spacetime, the FRW universe, we extend the quantum tunneling method beyond semiclassical approximation. And the effect of Hawking radiation of the apparent horizon of the FRW universe is studied. In the form, we give out the high order correction terms of the Hawking temperature and the entropy. The Kodama vector plays a crucial role in the definition of energies of the radiation particles. We present our analysis under the FRW like coordinate system and the much-like to Painleve coordinate system, respectively. Secondly, based on the general analysis of tunneling method of the static spacetime, where the tunneling rateΓ- exp(△S) arises as a consequence of the first law of thermodynamics for horizons holds the form dE_H = TdS + PdV, we develop the general method in the dynamical spacetime, the FRW universe. However, there are many differences between the static and the dynamical spcetimes. Using the the general analysis, from the unified first law of thermodynamics dE_H = TdS+WdV(where W = (ρ- P)/2) on the apparent horizon, we study the effect of Hawking radiation of the apparent horizon of the FRW universe. In such a dynamical system and in the view of the Kodama vector, we find that the tunneling rateΓ- exp(-△S) of the Hawking radiation also arises as a consequence of the unified first law of thermodynamics on horizons.In the end, using the Kodama-Hayward dynamical black hole theory, we study two dynamical black hole modes, the Vaidya black hole and the McVittie black hole, and the effects of Hawking radiation are analyzed. For the Vaidya black hole, we find the general analysis of tunneling method follows well, the tunneling rate can be given out, thus the emission spectrum. For the McVittie black hole, we give out the form of the unified first law of thermodynamics on the apparent horizon, and we find that there exists the ingoing mode of Hawking radiation. However as a black hole, the physical meaning of the radiation of the ingoing mode is unclear and even puzzling. We believe that the dynamic characteristics of the McVittie black hole come from the dynamic performances of the background spacetime, the FRW universe. In this sense, the McVittie spacetime may also not actually be viewed as a dynamical black hole, despite its resemblance.