黑洞费米子量子隧穿的量子引力修正

发布时间：2018-02-23 05:43

本文关键词： 黑洞量子引力霍金蒸发量子隧穿　出处：《兰州大学》2015年硕士论文　论文类型：学位论文

【摘要】：各种量子引力理论都一致地预言存在最小可测量长度。黑洞一直是研究量子引力理论的很好的系统。霍金运用弯曲时空量子场论证明了黑洞存在辐射谱为纯热谱的辐射。虽然Per Kraus、Frank Wilczek和Maulik K.Parikh等人提出了霍金辐射的量子隧穿方法并得到了很好的修正结果,但是这并没有考虑量子引力最小可测量长度的影响。目前已有文献利用广义不确定性原理研究了黑洞霍金辐射的量子引力效应。这对理论上探讨黑洞是否存在蒸发剩余和黑洞信息丢失疑难具有深远的意义。我们采用了新的量子引力修正方案和量子隧穿半经典的Hamilton-Jacobi方法对黑洞费米子隧穿的量子引力修正作了研究并得到了有意义的结果。第一章主要介绍关于黑洞和霍金辐射的背景知识。其中重点介绍了量子隧穿霍金辐射的物理原理,以及量子隧穿霍金辐射的测地线方法和Hamilton-Jacobi方法。第二章介绍量子引力中的最小可测量长度和提出新的量子引力修正方案。各种量子引力理论都一致地预言存在最小可测量长度。在理论上引入量子引力最小可测量长度的方法之一是利用广义的不确定性原理(GUP)。因此我们利用GUP提出了更加合理有效的量子引力修正方案。第三章运用半经典Hamilton-Jacobi方法和新的量子引力修正方案,依次对Schwarzsc-hild黑洞、Reissner-Nordstrom黑洞、Kerr黑洞和Kerr-Newman de Sitter黑洞中费米子在黑洞视界的隧穿问题作了研究。其中对前三者的研究表明,量子引力效应不仅会使黑洞费米子辐射谱偏离纯热谱,而且会减缓黑洞的蒸发乃至产生蒸发剩余。对Kerr-Newman de Sitter黑洞的研究不仅得到了量子引力修正的隧穿概率和辐射温度,而且精确验证了前面三种黑洞修正结果的正确性和直接得到了Kerr-Newman黑洞情形的修正结果。为了计算方便和着重考察量子引力效应对黑洞费米子辐射的影响,我们暂时没有考虑辐射粒子对时空的反作用。第四章对整篇工作做一总结和展望。
[Abstract]:All kinds of quantum gravitation theories have consistently predicted the existence of the minimum measurable length. Black hole has always been a good system for studying quantum gravity theory. Hawking proved that the existence of radiation spectrum of black hole is pure thermal spectrum by using the theory of curved space-time quantum field. Although Per Krausch Frank Wilczek and Maulik K. Parikh et al proposed a quantum tunneling method for Hawking radiation and obtained very good results. However, this does not take into account the influence of the minimum measurable length of quantum gravity. At present, some literatures have studied the quantum gravitational effect of Hawking radiation in black hole by using generalized uncertainty principle. The problem of residual and information loss of black hole is of great significance. A new scheme of quantum gravity correction and a semi-classical Hamilton-Jacobi method of quantum tunneling are used to study the quantum gravitational correction of fermion tunneling in black hole. The first chapter mainly introduces the background knowledge about black hole and Hawking radiation, which focuses on the physical principle of quantum tunneling Hawking radiation. And geodesic method and Hamilton-Jacobi method for quantum tunneling Hawking radiation. Chapter 2 introduces the minimum measurable length of quantum gravity and proposes a new scheme of quantum gravity correction. One of the methods to introduce the minimum measurable length of quantum gravity in theory is to use the generalized uncertainty principle. Therefore, we propose a more reasonable and effective scheme of quantum gravity correction by using GUP. The chapter uses the semi-classical Hamilton-Jacobi method and a new quantum gravity correction scheme. The tunneling of fermions at the event horizon of the Schwarzsc-hild black hole Reissner-Nordstrom black hole and the Kerr-Newman de Sitter black hole is studied in turn. The study of Kerr-Newman de Sitter black hole not only obtained the modified tunneling probability and radiation temperature of quantum gravity, but also slowed down the evaporation of black hole. Moreover, the correction results of the first three kinds of black holes are verified accurately and the modified results in the case of Kerr-Newman black holes are obtained directly. The effect of quantum gravitational effect on the fermion radiation of black holes is investigated in order to facilitate the calculation. For the time being, we do not consider the reaction of radioactive particles to time and space. Chapter 4th gives a summary and prospect of the whole work.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P145.8

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