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姓名 鄒守峻(Shou-jyun Zou)  查詢紙本館藏   畢業系所 物理學系
論文名稱 自引力球殼穿隧的Hawking輻射
(Hawking Radiation as Tunneling of Self-gravitating Shell)
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摘要(中) 量子力學告訴人們,任何物理演化過程應該滿足因果律:
信息是守恆的,即信息不會丟失。早期的研究指出黑洞向外蒸
發物質是熱輻射過程,人們無法從被輻射出來的物質中提取形
成黑洞物質的任何信息。那麼有關形成黑洞的物質的信息去哪
兒了呢?
Parikh 和Wilczek用量子穿隧的方法,並且考慮總系統能
量守恆討論了Schwarzschild 黑洞的幅射率,得出非純熱譜的
Hawking 幅射,此結果暗示黑洞幅射過程訊息守恆的可能性。
本文主要以球殼模型及Parikh-Wilczek 的量子穿隧法討論
Hawking 幅射率。第二章介紹Parikh-Wilczek 所做的計算,此
計算採用Painlevé-Gullstrand 座標系。第三章討論度規(gμν)在
視界處不發散的情況下,用量子穿隧法計算的結果不隨座標選
取而改變。第四章我們討論有靜止質量的Hawking 幅射,為此
目標我們採用自引力的球殼模型,因為此模型本身即有總系統
能量守恆的性質,最後我們也得出同樣非純熱譜的Hawking幅
射率。第五章我們利用相同的方法對Kerr-Newman黑洞做計
算,得出幅射的修正譜,其結果支持黑洞幅射過程訊息守恆。
摘要(英) Hawking and Bekenstein made a remarkable connection between thermodynamics, quantum mechanics and black holes which predicted that black holes will slowly radiate away. But this theory violated the laws of quantum mechanics and created a contradiction known as the ”information paradox”. We have studied the Hawking radiation as a semiclassical tunneling process. Using the method proposed by Parikh and Wilczek, the calculation indicates that the black hole radiation contains a correction to the thermal spectrum. This result suggests a possibility of informationcarrying correlations in the radiation. In chaper 3, we have verified that, for nonrotating cases, the tunneling calculation will give the same result if the black hole metric is smooth at horizon. In chapter 4, we verify the tunneling approach by an other possible picture that that the radiation contains many tiny self-gravitating shells whose dynamics is determined by the effective action. In chaper 5, we have calculated the coaxial rotating radiation in Kerr-Newman black hole.
關鍵字(中) ★ 穿隧
★ 輻射
★ 黑洞
關鍵字(英) ★ Hawking Radiation
★ Tunneling
★ Black hole
論文目次 1 Introduction 1
1.1 Black hole .. . . . . . . . . . . . . . . . . . . . . 1
1.2 Black hole thermodynamics . . . . . . . . . . . . . . 2
1.3 Hawking radiation and black hole information . . . . 4
2 Hawking Radiation as Tunneling 7
2.1 Painlev´e coordinates . . . . . . . . . . . . . . . . 7
2.2 WKB approximation . . . . . . . . . .. . . . . . . . 9
2.3 Emission rate . . . . . . . . . . . . . . . . . . . . 10
3 Tunneling in Different Coordinates 12
3.1 Schwarzschild coordinates . . . . . . . . . . . . . . 12
3.2 Eddington-Finkelstein coordinates . . . . . . . . . . 13
3.3 Metrics with regular horizon . . . . . . . . . . . . 14
4 The Self-gravitating Shell 16
4.1 Shell system . . . . . . . . . . . . . .. . . . . . . 16
4.2 Schwarzschild background in Painlev´e coordinates . 17
4.3 Black hole radiation . . . .. . . . . . . . . . . . . 20
5 Radiation of Rotating Black Holes 24
5.1 Kerr-Newman black hole .. . . . . . . . . . . . . . . 24
5.2 Coaxial rotating shell .. . . . . . . . . . . . . . . 25
5.3 Coordinate dependence . . . ... . . . . . . . . . . . 28
6 Conclusion 30
Bibliography 31
A Mathematical Details 33
A.1 Reducing action from (4.2) to (4.3) . . . . . . . . . 33
A.2 Average of extrinsic curvature . . . . . . .. . . . . 36
A.3 Derivation of the effective action (4.4) . . . . . . .37
參考文獻 [1] S. W. Hawking, “Black holes explosions,” Nature. 248, 30 (1974).
[2] M. K. Parikh and F. Wilczek, “Hawking radiation as tunneling,” Phys. Rev. Lett. 85, 5042 (2000) [arXiv:hep-th/9907001].
[3] R. P. Kerr, “Gravitiational field of a spinning mass as an example of algebraically special metrics,” Phys. Rev. Lett. 11, 237 (1963).
[4] E. T. Newman, R. Couch, K. Chinnapared, A. Exton, A. Prakash, and R. Torrence, “Metric of a Rotating, Charged Mass,” J. Math. Phys. 6, 918 (1965).
[5] B. Carter, “Axisymmetric black hole has only two degrees of freedom,” Phys. Rev. Lett. 26, 331 (1971).
[6] S. W. Hawking, “Gravitational radiation form colliding black holes,” Phys. Rev. Lett. 26, 1344 (1971).
[7] J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D. 7, 2333 (1973) [arXiv:hep-th/9306083].
[8] J. M. Bardeen, B. Carter, S. W. Hawking, “The four laws of black hole mechanics,” Comm. Math. Phys. 31, 161 (1973).
[9] S. W. Hawking, “Breakdown of predictability in gravitational collapse,” Phys. Rev. D14, 2460 (1976).
[10] D. N. Page, “Information in black hole radiation,” Phys. Rev. Lett. 71, 3743 (1993) [arXiv:hep-th/9306083].
31
[11] M. K. Parikh, “Energy conservation and Hawking radiation,” arXiv:hepth/ 0402166.
[12] S. W. Hawking, “Particle creation by black holes,” Comm. Math. Phys. 43, 199 (1975).
[13] G. W. Gibbons, S. W. Hawking, “Action integrals and partition functions in quantum gravity,” Phys. Rev. D15, 2752 (1977).
[14] P. Painlev´e, “La mecanique classique el la theorie de la relativite,” C. R. Acad. Sci. (Paris) 173, 677 (1921).
[15] A. Gullstrand, “Allegemeine lLorper-problems in der Einsteinshen osung des statischen einkL gravitations theorie,” Arkiv. Mat. Astron. Fys. 16(8), 1 (1922).
[16] E. Keski-Vakkuri and P. Kraus, “Microcanonical D-branes and back reaction,” Nucl. Phys. B 491, 249 (1997) [arXiv:hep-th/9610045].
[17] V. D. Gladush, “The variational principle for dust shells,” J. Math. Phys. 42, 2590 (2001) [arXiv:gr-qc/0001073].
[18] X. n. Wu and S. Gao, “Tunneling effect near weakly isolated horizon,” Phys. Rev. D 75, 044027 (2007) [arXiv:gr-qc/0702033].
[19] P. K. Townsend, “Black holes,” arXiv:gr-qc/9707012.
[20] J. Y. Zhang and Z. Zhao, “New coordinates for Kerr-Newman black hole radiation,” Phys. Lett. B 618, 14 (2005).
指導教授 陳江梅(Chiang-Mei Chen) 審核日期 2007-6-20
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