紅外修正的Horava引力理論研究
發(fā)布時間：2018-12-21 13:30
【摘要】：最近,Horava利用Lifshitz標度提出了一個紫外區(qū)具有完善性質的引力理論。為了滿足重整化,該理論在紫外區(qū)放棄Lorentz對稱性并引入高階度規(guī)導數(shù)從而得到非相對論的冪次計數(shù)重整化引力理論。該理論被稱為Horava引力理論或簡寫成HL引力。此后,為了在低能量區(qū)得到閔氏真空,Kehagias和Sfetsos (KS)引入與三維幾何中里契標量相關的項得到了靜態(tài)球對稱的漸近平坦黑洞解,該解也被稱為紅外修正Horava引力中的黑洞,本文簡稱KS黑洞。 本論文以KS黑洞為研究對象,詳細研究其霍金輻射、似正規(guī)模、光線偏折和量子統(tǒng)計熵等內容。 在第一章中,論文主要論述了與黑洞和Horava引力等相關的背景知識。 在第二章中,論文首先用測地線方法得到了黑洞視界面處的霍金輻射譜,結果發(fā)現(xiàn)真實的輻射譜偏離純熱譜且與輻射粒子的質量無關。其次借助復路徑分方法得到視界面處費米子的隧穿率,并找到隧穿率與視界溫度之間的關系。 在第三章中,論文分別利用三階和六階WKB數(shù)值方法,得到了費米場擾動的低模頻率。結果發(fā)現(xiàn)：當引力參數(shù)α和角動量數(shù)k固定時,模數(shù)n越大,費米場振動越慢,衰減越快；當固定k和n時,α越大,費米場振動越慢,衰減越快。因此,與普通的Schwarzschild黑洞相比,KS黑洞中的費米場將衰減得更慢。 在第四章中,論文利用作用量分析法得到了黑洞時空中光線偏折角的解析表達式,并結合天文觀測(long-baseline radio interferometry、Jupiter measurement、 Hipparcos satellite)給出了太陽、木星、地球等系統(tǒng)對參數(shù)α的限制。 在第五章中,論文利用廣義測不準原理(Generalized Uncertainty Principle,GUP)與’t Hooft的磚墻方法(Brick Wall Method, BWM)兩種方法分別研究了黑洞的量子統(tǒng)計熵。研究發(fā)現(xiàn)如果適當調節(jié)能層厚度或者適當?shù)剡x取截斷因子,黑洞熵可以回到Bekenstein面積熵的形式。 以上研究結果提供了尋找KS黑洞的依據(jù),為將來更詳細地研究該黑洞提供豐富的參考資料,也促使我們更充分地理解Horava引力理論。
[Abstract]:Recently, Horava proposed a theory of gravity with perfect properties in ultraviolet region by using Lifshitz scale. In order to satisfy renormalization, the theory gives up Lorentz symmetry in ultraviolet region and introduces higher order metric derivative to obtain the nonrelativistic power counting renormalization gravity theory. This theory is known as the Horava Gravity Theory, or HL Gravity. Subsequently, in order to obtain Mins vacuum in the low energy region, Kehagias and Sfetsos (KS) introduce the terms related to the Ricci scalar in 3D geometry to obtain the asymptotically flat black hole solution of static spherical symmetry, which is also called the black hole in the infrared modified Horava gravity. This paper is referred to as KS black hole. In this paper, the Hawking radiation, positive scale, light deflection and quantum statistical entropy of KS black hole are studied in detail. In the first chapter, the background knowledge related to black hole and Horava gravity is discussed. In the second chapter, the Hawking spectrum at the black hole's apparent interface is obtained by geodesic method. It is found that the true spectrum deviates from the pure thermal spectrum and is independent of the mass of the radioactive particles. Secondly, the tunneling rate of fermion at the apparent interface is obtained by using the method of complex path separation, and the relationship between tunneling rate and horizon temperature is found. In the third chapter, the low mode frequency of Fermi field perturbation is obtained by using the third-order and sixth-order WKB numerical methods, respectively. The results show that when the gravitational parameter 偽 and the angular momentum number k are fixed, the larger the modulus n is, the slower the Fermi field vibration is and the faster the attenuation is, while the larger 偽 is fixed at k and n, the slower the Fermi field vibration is and the faster the attenuation is. Therefore, the Fermi field in the KS black hole will decay more slowly than the ordinary Schwarzschild black hole. In chapter 4, the analytical expression of light deflection angle in black hole space-time is obtained by using the action quantity analysis method, and the sun, Jupiter and Jupiter are given with astronomical observations (long-baseline radio interferometry,Jupiter measurement, Hipparcos satellite). The limit of the parameter 偽 of the Earth and other systems. In chapter 5, the quantum statistical entropy of black hole is studied by using the generalized uncertainty principle (Generalized Uncertainty Principle,GUP) and the brick wall method (Brick Wall Method, BWM) of't Hooft. It is found that if the energy layer thickness is adjusted properly or the truncation factor is properly selected, the black hole entropy can return to the form of Bekenstein area entropy. The above results provide the basis for finding KS black hole, provide abundant reference materials for further detailed study of the black hole, and promote us to fully understand Horava's theory of gravity.
【學位授予單位】：信陽師范學院
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：P145.8
本文編號：2388973
[Abstract]:Recently, Horava proposed a theory of gravity with perfect properties in ultraviolet region by using Lifshitz scale. In order to satisfy renormalization, the theory gives up Lorentz symmetry in ultraviolet region and introduces higher order metric derivative to obtain the nonrelativistic power counting renormalization gravity theory. This theory is known as the Horava Gravity Theory, or HL Gravity. Subsequently, in order to obtain Mins vacuum in the low energy region, Kehagias and Sfetsos (KS) introduce the terms related to the Ricci scalar in 3D geometry to obtain the asymptotically flat black hole solution of static spherical symmetry, which is also called the black hole in the infrared modified Horava gravity. This paper is referred to as KS black hole. In this paper, the Hawking radiation, positive scale, light deflection and quantum statistical entropy of KS black hole are studied in detail. In the first chapter, the background knowledge related to black hole and Horava gravity is discussed. In the second chapter, the Hawking spectrum at the black hole's apparent interface is obtained by geodesic method. It is found that the true spectrum deviates from the pure thermal spectrum and is independent of the mass of the radioactive particles. Secondly, the tunneling rate of fermion at the apparent interface is obtained by using the method of complex path separation, and the relationship between tunneling rate and horizon temperature is found. In the third chapter, the low mode frequency of Fermi field perturbation is obtained by using the third-order and sixth-order WKB numerical methods, respectively. The results show that when the gravitational parameter 偽 and the angular momentum number k are fixed, the larger the modulus n is, the slower the Fermi field vibration is and the faster the attenuation is, while the larger 偽 is fixed at k and n, the slower the Fermi field vibration is and the faster the attenuation is. Therefore, the Fermi field in the KS black hole will decay more slowly than the ordinary Schwarzschild black hole. In chapter 4, the analytical expression of light deflection angle in black hole space-time is obtained by using the action quantity analysis method, and the sun, Jupiter and Jupiter are given with astronomical observations (long-baseline radio interferometry,Jupiter measurement, Hipparcos satellite). The limit of the parameter 偽 of the Earth and other systems. In chapter 5, the quantum statistical entropy of black hole is studied by using the generalized uncertainty principle (Generalized Uncertainty Principle,GUP) and the brick wall method (Brick Wall Method, BWM) of't Hooft. It is found that if the energy layer thickness is adjusted properly or the truncation factor is properly selected, the black hole entropy can return to the form of Bekenstein area entropy. The above results provide the basis for finding KS black hole, provide abundant reference materials for further detailed study of the black hole, and promote us to fully understand Horava's theory of gravity.
【學位授予單位】：信陽師范學院
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：P145.8
【參考文獻】
相關博士學位論文 前3條
1 陳松柏;黑洞時空中的似正規(guī)模和冪率拖尾[D];湖南師范大學;2006年
2 劉墨林;基于空間—時間—物質理論和膜世界模型的黑洞研究[D];大連理工大學;2009年
3 蔣青權;量子隧穿、反常與黑洞霍金輻射[D];華中師范大學;2009年
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