【作者】 江克侠；

【导师】 岳瑞宏； 彭丹涛；

【作者基本信息】 西北大学 ， 理论物理， 2009， 博士

【摘要】 引力和视界热力学的关系是理论物理中非常令人感兴趣的问题之一。更为重要的是,近年来联系于视界热力学一些新的性质被发现:Einstein方程在视界上可以作为热力学第一定律的形式出现;在Friedmann-Robertson-Walker(FRW)宇宙表观视界上,时空动力学方程(Friedmann方程)也可以写成一个所谓的统一热力学第一定律的形式;局域定义的FRW宇宙表观视界,也存在着在Kodama矢量观测者看来的Hawking辐射效应。Hawking辐射是黑洞物理极其重要的一个量子现象,Parikh和Wilczek进一步整理和推广了Keski-Vakkuri和Kraus把辐射解释为粒子经过视界势垒隧穿的思想,称为辐射的Parikh-Wilczek隧穿方法。本文进一步研究了动力学时空FRW宇宙表观视界的Hawking辐射效应,以及动态黑洞模型-Vaidya黑洞和McVittie黑洞表观视界上的热力学,探讨了辐射和视界热力学的关系。首先,在动力学时空FRW宇宙背景下,发展了超半经典近似的量子隧穿方法,研究了FRW宇宙表观视界的Hawking辐射效应,形式上给出了Hawking温度和熵的高阶量子修正项,Kodama矢量对定义辐射粒子的能量起着关键作用,我们分别用FRW坐标以及类Painlevé坐标给出了详细的分析。其次,基于静态黑洞时空隧穿方法的一般性研究,那里黑洞的辐射率Γ-exp(ΔS),是视界上热力学第一定律dE_H=TdS+PdV的必然结果,我们在动力学时空FRW宇宙背景下,发展了这种分析。动力学时空与静态时空有着很大不同,我们采用一般性分析方法,从视界上统一热力学第一定律dE_H=TdS+WdV(其中W=(p-P)/2)出发,研究了FRW宇宙表观视界的Hawking辐射效应,形象的表明了在动力学时空下,Kodama矢量观测者意义下的Hawking辐射率Γ-exp(-ΔS),也是其视界热力学第一定律的必然结果。最后,利用Kodama-Hayward动态黑洞理论,我们研究了两个动态黑洞模型-Vaidya黑洞和McVittie黑洞,分析了表观视界上Hawking辐射。发现对Vaidya黑洞,隧穿方法的一般性分析可以很好的给出辐射率,从而给出辐射谱;对于McVittie黑洞,我们给出了表观视界上的统一热力学第一定律形式,分析发现McVittie黑洞存在内行模式的Hawking辐射效应,这从物理上是难以理解的。我们认为McVittie黑洞的动态特性来源于背景时空FRW宇宙的动态因素,从这个角度也说明了McVittie解并不是严格意义上的动态黑洞解。更多还原

【Abstract】 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.更多还原