引力场中的轨道效应和黑洞的量子隧穿效应
|
摘要
随着广义相对论引力效应不断被实验观测所验证,Einstein的广义相对论已成为公认的经典理论。同时,随着科学技术的发展,更多的引力效应被观测到和被验证。引力场中的轨道效应就是其中的一类。其极限情况光子的轨道效应(引力场中光线的偏转)更是广义相对论的四大经典实验验证之一。
在第二章中,我们运用一种优美的数学方法,计算了带有电荷和整体单极子的中心质量的引力场中的轨道进动效应。通过对所得结果的分析,我们发现,由于整体对称性破缺,轨道进动效应将增强,但由场源的电荷引起的轨道进动效应削弱了由场源的质量引起的相应效应。我们推广了Schwarzschild场中的轨道效应,通过对天体参数的讨论,得到了相应天体的轨道进动效应,为广义相对论提供了一种可能的实验验证。我们还计算了带有电荷和磁荷的旋转场源外部稳态时空中光子的轨道效应。通过对所得结果的分析,我们发现电荷所引起的光子轨道偏转效应减小了由场源质量所引起的光子轨道偏转效应,但由场源的旋转所引起的相应偏转效应依赖于源的旋转方向与光子运动方向之间的夹角。我们通过对相应的天体参数的讨论得到了一系列有意义的结果。
第三章介绍了黑洞基本热力学性质,并分别运用Bogoliubov法和Damour-Ruffini(D-R)方法证明了黑洞存在热辐射—Hawking辐射。第四章研究了黑洞的量子隧穿效应—将Hawking辐射看成穿过视界的隧穿过程,进行了直接的推导,得到了隧穿效率表达式。我们运用Keski-Vakkuri, Kraus and Wilczek(KKW)的分析方法计算被暗能量包围的黑洞的温度和熵,其温度和熵不同于相应的Hawking温度和Bekenstein-Hawking熵。我们得到的结果提供了一种处理信息疑难的可能机制—因为该辐射谱不再是纯热谱。
最后,我们运用由Banerjee和Majhi所发展的非WKB近似的Hamiliton-Jacobi方法,计算了被暗能量包围的黑洞的温度和熵,即修正后的温度和熵。
Einstein's general relativity was known as the classical theory with more gravitational effects of the general relativity continuously proved by experimental observation facts. At the same time, more gravitational effects are observed and proved with the development of the science and the technology. The orbital effect in the gravitational field is one of them, the limiting case, the photon orbital effect the deflection of light lay in the gravitational field, which is one of the four classical experimental verifications of the general relativity.
First, using an elegant mathematical method we calculate the orbital effects in the gravitational field of the centre with electric charge and a global monopole. Analyzing the results, we obtain that the orbital precession effect increases on account of the global symmetry breaking, but the orbital precession effect aroused by the electric charge of the field source reduces the orbital precession effect aroused by the mass of the field source. We generalize the effect in the Schwarzschild field, and obtain the celestial body orbital effect by discussing the parameters of it, which provides a feasible experi-mental verification of the general relativity. Then, we calculate the orbital effect of photon in the general stationary spacetime created by the spinning mass with electric charge and a large number of mag-netic monopoles. By analyzing the result we find that the deflection effect caused by the electric charge and magnetic charge decreases the deflection effect caused by the mass of the field source, but the deflection effect caused by the spinning of the field source depends on the angle between the spinning direction of the field source mass and the direction of photon motion. We obtain a series of interesting results by discussing the parameters of the celestial body.
Second, we introduce the basic thermal nature of the black hole, then used the Bogoliubov method and the Damour-Ruffini(D-R) method, and proved that the black holes have thermal radiation—Hawking radiation. We study the quantum tunneling effect of the black hole, namely regarding Hawking radiation as a tunneling pro-cess across the horizon through a short and direct derivation then ob-tain the expression of the tunneling rate. We use the Keski-Vakkuri, Kraus and Wilczek(KKW) analysis to calculate the temperature and entropy of the black hole surrounded by Quintessence and obtain the temperature and entropy are different from the Hawking tempera-ture and the Bekinstein-Hawking entropy. The result we get can offer a possible mechanism to deal with the information loss paradox because the spectrum is not purely thermal.
Finally, we use non-WKB approximation Hamilton-Jacobi method which was developed by Benerjee and Majhi. And calculate the tem-perature and entropy of the black hole surrounded by Quintessence, i.e. the corrected temperature and entropy.
在第二章中,我们运用一种优美的数学方法,计算了带有电荷和整体单极子的中心质量的引力场中的轨道进动效应。通过对所得结果的分析,我们发现,由于整体对称性破缺,轨道进动效应将增强,但由场源的电荷引起的轨道进动效应削弱了由场源的质量引起的相应效应。我们推广了Schwarzschild场中的轨道效应,通过对天体参数的讨论,得到了相应天体的轨道进动效应,为广义相对论提供了一种可能的实验验证。我们还计算了带有电荷和磁荷的旋转场源外部稳态时空中光子的轨道效应。通过对所得结果的分析,我们发现电荷所引起的光子轨道偏转效应减小了由场源质量所引起的光子轨道偏转效应,但由场源的旋转所引起的相应偏转效应依赖于源的旋转方向与光子运动方向之间的夹角。我们通过对相应的天体参数的讨论得到了一系列有意义的结果。
第三章介绍了黑洞基本热力学性质,并分别运用Bogoliubov法和Damour-Ruffini(D-R)方法证明了黑洞存在热辐射—Hawking辐射。第四章研究了黑洞的量子隧穿效应—将Hawking辐射看成穿过视界的隧穿过程,进行了直接的推导,得到了隧穿效率表达式。我们运用Keski-Vakkuri, Kraus and Wilczek(KKW)的分析方法计算被暗能量包围的黑洞的温度和熵,其温度和熵不同于相应的Hawking温度和Bekenstein-Hawking熵。我们得到的结果提供了一种处理信息疑难的可能机制—因为该辐射谱不再是纯热谱。
最后,我们运用由Banerjee和Majhi所发展的非WKB近似的Hamiliton-Jacobi方法,计算了被暗能量包围的黑洞的温度和熵,即修正后的温度和熵。
Einstein's general relativity was known as the classical theory with more gravitational effects of the general relativity continuously proved by experimental observation facts. At the same time, more gravitational effects are observed and proved with the development of the science and the technology. The orbital effect in the gravitational field is one of them, the limiting case, the photon orbital effect the deflection of light lay in the gravitational field, which is one of the four classical experimental verifications of the general relativity.
First, using an elegant mathematical method we calculate the orbital effects in the gravitational field of the centre with electric charge and a global monopole. Analyzing the results, we obtain that the orbital precession effect increases on account of the global symmetry breaking, but the orbital precession effect aroused by the electric charge of the field source reduces the orbital precession effect aroused by the mass of the field source. We generalize the effect in the Schwarzschild field, and obtain the celestial body orbital effect by discussing the parameters of it, which provides a feasible experi-mental verification of the general relativity. Then, we calculate the orbital effect of photon in the general stationary spacetime created by the spinning mass with electric charge and a large number of mag-netic monopoles. By analyzing the result we find that the deflection effect caused by the electric charge and magnetic charge decreases the deflection effect caused by the mass of the field source, but the deflection effect caused by the spinning of the field source depends on the angle between the spinning direction of the field source mass and the direction of photon motion. We obtain a series of interesting results by discussing the parameters of the celestial body.
Second, we introduce the basic thermal nature of the black hole, then used the Bogoliubov method and the Damour-Ruffini(D-R) method, and proved that the black holes have thermal radiation—Hawking radiation. We study the quantum tunneling effect of the black hole, namely regarding Hawking radiation as a tunneling pro-cess across the horizon through a short and direct derivation then ob-tain the expression of the tunneling rate. We use the Keski-Vakkuri, Kraus and Wilczek(KKW) analysis to calculate the temperature and entropy of the black hole surrounded by Quintessence and obtain the temperature and entropy are different from the Hawking tempera-ture and the Bekinstein-Hawking entropy. The result we get can offer a possible mechanism to deal with the information loss paradox because the spectrum is not purely thermal.
Finally, we use non-WKB approximation Hamilton-Jacobi method which was developed by Benerjee and Majhi. And calculate the tem-perature and entropy of the black hole surrounded by Quintessence, i.e. the corrected temperature and entropy.
引文
[1]D. C. Cassidy, Uncertainty:the life and science of Werner Heisenberg[M], Freeman, New York, (1992).
[2]T. S. Kuhn Black-body theory and the quantum discontinuity[M], Clarendon, Ox-ford, (1978).
[3]曾谨言,量子力学[M],北京：科学出版社(第三版)第一卷(2000).
[4]P. A. M. Dirac The principles of quantum mechanics[M], Clarendon, Oxford, (1930).
[5]R. P. Feynman and A. R. Hibbs, Quantum mechanics and path integrals[M], New York, McGraw-Hill, (1992).
[6]王永久、唐智明,引力理论和引力效应[M],长沙：湖南科学技术出版社,(1990).
[7]T. W. B. Kibble, Topology of cosmic domains and strings[J], J. Phys. A 9,1387 (1976).
[8]A. Vilenkin, Cosmic strings,and domain walls [J], Phys. Rep.121,263 (1985).
[9]M. Barriola and A. Vilenkin, Gravitational Field of a Global Monopolc[J], Phys. Rev. Lett.63,341 (1989).
[10]S. Perlmutter et al., Measurements of Omega and Lambda from 42 High-Redshift Supernovae[J], ApJ 517,565 (1999).
[11]A. G. Riess ct al., Observational Evidence from Supernovac for an Accelerating Universe and a Cosmological Constant[J], AJ 116,1009 (1998).
[12]D. N. Spergel et al., First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations:Determination of Cosmological Parameters[J], ApJS 148,175 (2003).
[13]B. Ratra and P. E. J. Peebles, Cosmological consequences of a rolling homogeneous scalar field[J], Phys. Rev. D 37,3406 (1988).
[14]R. R. Caldwell, R. Dave, and P. J. Steinhardt, Cosmological Imprint of an Energy Component with General Equation of Statc[J], Phys. Rev. Lett.80,1582 (1998).
[15]R. R. Caldwell, A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state [J], Phys. Lett. B 545,23 (2002).
[16]B. Feng, X. L. Wang and X. M. Zhang, Dark Energy Constraints from the Cosmic Age and Supernova[J], Phys. Lett. B 607,35 (2005).
[17]B. Feng, M. Z. Li, Y. S. Piao and X. Zhang, Oscillating Quintom and the Recurrent Universe[J], Phys. Lett. B 634,101 (2006).
[18]G. Zhao, J. Xia, M. Li, B. Feng, X. Zhang, Perturbations of the Quintom Models of Dark Energy and the Effects on Observations[J], Phys. Rev. D 72,123515 (2005).
[19]R. H. Dicke, Eotvos Experiment and the Gravitational Red Shift [J], Am. J. Phys. 28,344 (1960).
[20]L. I. Schiff, Possible new experimental test of general relativity theory[J], Phys. Rev. Lett.4,215 (1960).
[21]D. K.Ross and L. I. Schiff, Analysis of the proposed planetary radar reflection experiment[J], Phys. Rev.141,1215 (1966).
[22]I. I. Shapiro, Testing general relativity with radar[J], Phys. Rev.141,1219 (1966).
[23]B. B. Godfrey, Mach's Principle, the Kerr Metric, and Black Holc Physics[J], Phys. Rev. D 1,2721 (1970).
[24]J. K. Chose and P. Kumar, Gravitational mass defect in general relativity [J], Phys. Rev. D 13,2736 (1976).
[25]D. C. Wilkins, Bound Geodesies in the Kerr Mctric[J], Phys. Rev. D 5,814 (1972).
[26]P. H. Hu and Y. J. Wang, Repulsive effects in steady axisymmetric fields[J], Chin. Phys.15,1120 (2006).
[27]Chen J H, Wang Y J Gravitational frequency-shift and deflection of light by Quintessence[J], Chin. Phys.16,3212 (2007).
[28]T. X. Gong, A. G. Li. and Y. J. Wang, Gravitational effect of centre mass with electric charge and a large number of magnetic monopolcs[J], Chin. Phys.14(4), 859 (2005).
[29]王永久, 荷电天体的引力质量亏损[J].湖南师范大学自然科学学报04,29(2001).
[30]X. J. Huang and Y. J. Wang Mass-Defect Effect in the Hellings-Nordtvedt Field[J], Chin. Phys. Lett.19(6),755 (2002).
[31]龚添喜、王永久, 球对称度规场中的质量亏损效应[J].湖南师范大学自然科学学报27(03),39(2004).
[32]T. X. Gong and Y. J. Wang, Mass defect effect in the gravitational field[J], Chin. Phys.14(1),45 (2005).
[33]王永久、唐智明,质量四极矩场中的轨道进动效应[J],50(12)2284(2001).
[34]T. X. Gong and Y. J. Wang, Orbital effect in the stationary axisymmetric field[J], Chin. Phys. B 17(7),2356 (2008).
[35]罗新炼、王永久、程立伟, 旋转荷电球体外部引力场中引力效应[J],物理学报46,846(1997).
[36]T. X. Gong and Y. J. Wang, Orbital Precession Effect in the Reissner-Nordstrom Field with a Global Monopole[J], Chin. Phys. Lett.26(3),030402 (2009).
[37]K. S. Virbhadra and G. F. R. Ellis, Schwarzschild black hole lensing[J], Phys. Rev. D 62,084003 (2000).
[38]K. Lake, Bending of light and the cosmological constant[J], Phys. Rev. D 65,087301 (2002).
[39]W. Rindler and M. Ishak, Contribution of the cosmological constant to the rela-tivistic bending of light revisited[J], Phys. Rev. D 76,043006 (2007).
[40]Y. Eriguchi and K. Nomoto, DOUBLE IMAGES OF THE SUPERNOVA 1987A BY THE GRAVITATIONAL LENS [J], Mod. Phys. Lett. A 2,645 (1987).
[41]龚添喜、王永久,一般稳态时空中光子的轨道效应[J].物理学报58,5988(2009).
[42]王永久、彭秋和,一种新型超巨质量(非黑洞)致密天体[J]，科学通报30(6),418(1985).
[43]刘辽、裴寿镛,量子史瓦茨黑洞和暗物质[J],物理学报55,4980(2006).
[44]王永久,经典黑洞和量子黑洞[M],北京：科学出版社(2008).
[45]Q. Y. Pan and J. L. Jing, Quasinormal modes of a stationary axisymmetric EMDA black hole[J], Chin. Phys.15,77 (2006).
[46]M. Sereno New interactions in the dark sector mediated by dark energy[J], Phys. Rev. D 77,043004 (2008).
[47]R. P. Kerr, Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics[J] Phys. Rev. Lett.11,237 (1963).
[48]E. T. Newman and A. I. Janis, Note on the Kerr spinning - particle metric[J] Math. Phys.6,344 (1965).
[49]M. Kasuya, Exact solution of a rotating dyon black hole[J], Phys. Rev. D 25,995 (1982).
[50]王永久,磁场中的旋转双荷黑洞[J]，物理学报33,1728(1984).
[51]P. A. M. Driac, Quantised Singularities in the Electromagnetic Field[J], Proc. Roy. Soc.133,60 (1931).
[52]Harish-Chandra, Motion of an Electron in the Field of a Magnetic Pole[J], Phys. Rev.74,883 (1948).
[53]Y. J. Wang and Q. H. Peng, GRAVITATIONAL PROPERTIES OF THE NEU-TRON STAR WITH MAGNETIC CHARGE AND MAGNETIC MOMENT [J], Sci. Sin.4,422 (1985).
[54]杨波, 一般加速带电带磁的动态黑洞中标量场的熵[J],物理学报55,2614(2008).
[55]C. J. Gao and Y. G. Shen, De Broglie-Bohm Quantization of the Reissner-Nordstrom Black Hole with a Global Monopole in the Background of de Sitter Space-Time[J], Chin. Phys. Lett.19(4),477 (2002).
[56]S. W. Hawking Gravitational radiation from colliding black holes[J], Phys. Rev. Lett.26,1344 (1971).
[57]R. Penrose Structure of space-time[M], ed. by C. M. Dewitt and J. A. Wheeler, Battelle Rencontres:1967 Lectures in Mathematics and Physics, New York:Ben-jamin (1968).
[58]J. D. Bekenstein, Black Holes and Entropy[J], Phys. Rev. D 3,2333 (1973).
[59]刘辽、赵峥,广义相对论[M],(第二版)北京：高等教育出版社, (2004).
[60]S. W. Hawking, Black hole explosions[J], Nature 248,30 (1974).
[61]S. W. Hawking, Particle creation by black holes[J], Commun. Math. Phys.43,199 (1975).
[62]S. W. Hawking, Breakdown of predictability in gravitational collapse[J], Phys. Rev. D 14,2460 (1976).
[63]J. B. Hartle and S. W. Hawking, Path-integral derivation of black-hole radiance[J], Phys. Rev. D 13 2188 (1976).
[64]W. Isreal Thermo-field dynamics of black hole[J], Phys. Lett. A 57,107 (1976).
[65]G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity[J], Phys. Rev. D 15,2752 (1977).
[66]L. Parker The production of elementary particles by strong gravitational fields[M], ed. by F. P. Esposito and L. Witten, New York:Plenum press, (1977).
[67]赵峥, 黑洞的热性质与时空奇异性---零曲面附近的量子效应[M],北京：北京师范大学出版社,(1999).
[68]刘辽、许殿彦,Dirac粒子的Hawking蒸发[J],物理学报29,1617(1980).
[69]T. Damoar and R. Ruffini, Black-hole evaporation in the Klein-Sauter-Heisenberg-Eulcr formalism [J], Phys. Rev. D 14,332 (1976).
[70]N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space [M], Cambridge: Cambridge University Press (1982).
[71]M. K. Parikh, Energy conservation and Hawking radiation [J], Gen. Rel. Grav.36, 2419 (2004).
[72]M. K. Parikh and F. Wilczek, Hawking radiation as tunneling[J], Phys. Rev. Lett. 85,5042 (2000).
[73]M. K. Parikh, A secret tunnel through the horizon[J], Int. J. Mod. Phys.13,2351 (2004).
[74]S. Hemming and E. Keski-Vakkuri, Hawking radiation from AdS black holes[J], Phys. Rev. D 64,044006 (2001).
[75]A. J. Medved, Radiation via tunneling from a de Sitter cosmological horizon[J], Phys. Rev. D 66,124009 (2002).
[76]M. K. Parikh, New coordinates for de Sitter space and de Sitter radiation[J], Phys. Lett. B 546,189 (2002).
[77]G. Q. Li, Dilaton black hole tunneling radiation in dc Sitter universe [J], Commun. Theor. Phys.51,453 (2009).
[78]J. Y. Zhang and Z. Zhao, New coordinates for Kerr- Newman black hole radia-tion[J], Phys. Lett. B 618 14 (2005).
[79]J. Y. Zhang and Z. Zhao, Hawking radiation of charged particle via tunneling form the Reissner-Nordstrom black holc[J], JHEP 10,055 (2005).
[80]L. Gao and W. B. Liu, General radiation via tunneling in Kerr and Kerr- Newman black holes[J] Sci. Chin. G 51,1200 (2008).
[81]S. Iso, H. Umctsu and F. Wilczek, Hawking radiation from charged black holes via gauge and gravitational anomalics[J] Phys. Rev. Lett.96,151302 (2006).
[82]Y. W. Han, Quantum non-thermal effect, from Kerr- Newman black hole[J], Com-mun. Thcor. Phys.51,450 (2009).
[83]P. M. Garnavich, et al, Supernova limits on the cosmic equation of state[J], Astro-phys. J 509,74 (1998).
[84]Y. J. Wang and Z. M. Tang, Gravitational properties of an accelerating celestial body with a large number of monopoles[J], Astrophys. and S. S.282,363 (2002).
[85]S. B. Chen, B. Wang and R. K. Su, Hawking radiation in a d-dimensional static spherically symmetric black hole surrounded by Quintessence[J], Phys. Rev. D 77, 124011 (2008).
[86]J. L. Jing and Y. J. Wang and J.Y. Zhu, Generalized first law of thermodynamics for black holes in spacetimes which are not asymptotically flat[J], Phys. Lett. A 18731 (1994).
[87]J. H. Chen and Y. J. Wang, Influence of dark energy on gravitational time delay[J], Commun. Theor. Phys.50,101 (2008).
[88]V. V. Kiselev, Quintessence and black holes[J], Class. Quantum Grav.20 1187 (2003).
[89]P. Painleve, The stationary coordinates in a Schwarzschild blck hole[J], C. R. Acad. Sci.(Paris) 173,677 (1921).
[90]E. C. Vagenas, Generalization of the KKW analysis for black hole radiation [J], Phys. Lett. B 559,65 (2003).
[91]P. Kraus and F. Wilczek, Self-interaction.correction to black hole radiance [J], Nucl. Phys. B 433,403 (1995).
[92]P. Kraus and F. Wilcze k, Effect of self-interaction on charged black hole radi-ance[J], Nucl. Phys. B 437,231 (1995).
[93]E. Keski-Vakkuri and P. Kraus, Tunneling in a time- dependent setting[J], Phys. Rev. D 54,7407 (1996).
[94]S. M. Christcnscn and S. A. Fulling, Trace anomalies and the Hawking effect[J], Phys. Rev. D 15 2088 (1977).
[95]赵峥, 四维静态黎曼时空中的Hawking辐射[J]，物理学报30 1508(1981).
[96]杨波、赵峥,一般球对称动态时空中荷电Dirac粒子的Hawking辐射[J],物理学报43,858(1994).
[97]M. R. Setare and E. C. Vagenas, Self-gravitational corrections to the Cardy-Verlinde formula of the Achucarro-Ortiz black hole [J], Phys. Lett. B 584 127 (2004).
[98]A. J. Medved, Radiation via tunnelling in the charged BTZ black hole [J], Class. Quant. Grav.19,589 (2002).
[99]A. J. Medved and E. C. Vagenas, ON HAWKING RADIATION AS TUNNELING WITH BACK-REACTION [J], Mod. Phys. Lett. A 20,2449 (2005).
[100]M. Arzano, A. J. Medved and E. C. Vagenas, Hawking Radiation as Tunneling through the Quantum Horizon [J], JHEP 0509,037 (2005).
[101]M. R. Setare and E. C. Vagenas, Area Spectrum of Kerr and extremal Kerr Black Holes from Quasinormal Modes [J], Mod. Phys. Lett. A 20,1923 (2005).
[102]R. Kerner and R. B. Mann, Tunnelling, temperature, and Taub-NUT black holes[J], Phys. Rev. D 73,104010 (2006).
[103]J. Y. Zhang and Z. Zhao, New coordinates for Kerr-Newman black hole radiation [J], Phys. Lett. B 618,14 (2005).
[104]韩亦文,用量子隧穿法研究带质量四极矩静态黑洞的Hawking辐射[J]，物理学报54,5018(2005).
[105]胡亚鹏、张靖仪、.赵峥,Reissner-Nordstrom黑洞中带电粒子由隧穿导致的Hawking辐射的进一步讨论[J],物理学报56 0683(2007).
[106]Q. Q. Jing, S. Q. Wu and X. Cai, Hawking radiation from dilatonic black holes via anomalies [J], Phys. Rev. D 75,064029 (2007).
[107]R. Kerner and R. B. Mann, Tunnclling from Godcl black holes[J], Phys. Rev. D 75,084022 (2007).
[108]R. Li and J. R. Ren, Dirac particles tunneling from BTZ black hole [J], Phys. Lett. B 661 370 (2008).
[109]J. J. Peng and S. Q. Wu, Covariant anomalies and Hawking radiation from charged rotating black strings in anti-de Sitter spacetimes [J], Phys. Lett. B 661,300 (2008).
[110]R. Kerner and R. B. Mann, Charged fermions tunnelling from Kerr-Newman black holes [J], Phys. Lett. B 665 277 (2008).
[111]S. Das, P. Majumdar and R. K. Bhaduri, Absence of higher derivatives in the renormalization of propagators in quantum field theories with infinitely many cou-plings [J], Class. Quantum Grav.20,2355 (2002).
[112]Q. Q. Jing, Fermions tunnelling from GHS and non-extremal D1-D5 black holes [J], Phys. Lett. B 666,517 (2008).
[113]Z. Z. Ma, Hawking temperature of Kerr-Newman-AdS black hole from tunneling [J], Phys. Lett. B 666,376 (2008).
[114]B. Zhang, Q. Y. Cai and M. S. Zhan, Hawking radiation as tunneling derived from black hole thermodynamics through the quantum horizon [J], Phys. Lett. B 665, 260 (2008).
[115]X. K. He and W. B. Liu, Modified Hawking radiation in a BTZ black hole using Damour-Ruffini method [J], Phys. Lett. B 653,330 (2007).
[116]S. W. Zhou and W. B. Liu, Hawking radiation of charged Dirac particles from a Kerr-Newman black hole[J], Phys. Rev. D 77,104021 (2008).
[117]J. Y. Zhang, Black hole quantum tunnelling and black hole entropy correction [J], Phys. Lett. B 668,353 (2008).
[118]J. Y. Zhang and J. H. Fanm Hawking radiation via tunnelling from general sta-tionary axisymmetric black holes[J], Chin. Phys. B 16,3879 (2007).
[119]张靖仪、赵峥,电磁直线加速动态黑洞时空中Dirac粒子的Hawking辐射[J],物理学报52,2096(2003).
[120]刘文彪,Damour-Ruffini方法和Rcissncr-Nordstrom黑洞的非热Hawking辐射[J]，物理学报56,6164(2007).
[121]T. X. Gong and Y. J. Wang Quantum Non-thermal Effect from Black Holes Surrounded by Quintessence[J], Commun. Theor. Phys.52,974 (2009).
[122]D. V. Fursaev, Temperature and entropy of a quantum black hole and conformal anomaly[J], Phys. Rev. D 51, R5352 (1995).
[123]R. B. Mann and S. N. Solodukhin, Universality of Quantum Entropy for Extreme Black Holes [J], Nucl. Phys. B 523,293 (1998)
[124]R. K. Kaul and P. Majumdar, Logarithmic Correction to the Bekenstein-Hawking Entropy[J], Phys. Rev. Lett.84,5255 (2000).
[125]T. R. Govindarajan, R. K. Kaul and V. Suneeta, Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole[J], Class. Quantum Grav.18, 2877 (2001).
[126]S. S. More, Higher order corrections to black hole entropy[J], Class. Quantum Grav.22,4129 (2005).
[127]S. Mukherji and S. S. Pal, Logarithmic Corrections to Black Hole Entropy and AdS/CFT Correspondence [J], JHEP 0205,026 (2002).
[128]A. Ghosh and P. Mitra, An improved estimate of black hole entropy in the quantum geometry approach [J], Phys. Lett. B 616,114 (2005).
[129]D. N. Page, Hawking Radiation and Black Hole Thermodynamics[J], New Journal of Phys.7,203 (2005).
[130]R. Banerjee and B. R. Majhi, Quantum Tunneling Beyond Semiclassical Approx-imation [J], JHEP 0806,095 (2008).
[131]K Srinivasan and T Padmanabhan, Particle production and complex path analy-sis[J], Phys. Rev. D 60,024007 (1999).
[132]S K Modak, Corrected entropy of BTZ black hole in tunneling approach [J], Phys. Lett. B 671,167 (2009).
[133]P Mitra, Hawking temperature from tunnelling formalism [J], Phys. Lett. B 648, 240 (2007)
[134]J W York Jr, Black hole in thermal equilibrium with a scalar field:The back-reaction[J], Phys. Rev. D 31,775 (1985).
[135]C. O. Lousto and N. Sanchez, Back reaction effects in black hole spacetimes [J], Phys. Lett. B 212,411 (1988).
[136]J. M. Bardeen, B. Carter and S. W. Hawking, The four laws of black hole mechanics [J], Commun. Thcor. Phys.,31,161 (1973).
[2]T. S. Kuhn Black-body theory and the quantum discontinuity[M], Clarendon, Ox-ford, (1978).
[3]曾谨言,量子力学[M],北京：科学出版社(第三版)第一卷(2000).
[4]P. A. M. Dirac The principles of quantum mechanics[M], Clarendon, Oxford, (1930).
[5]R. P. Feynman and A. R. Hibbs, Quantum mechanics and path integrals[M], New York, McGraw-Hill, (1992).
[6]王永久、唐智明,引力理论和引力效应[M],长沙：湖南科学技术出版社,(1990).
[7]T. W. B. Kibble, Topology of cosmic domains and strings[J], J. Phys. A 9,1387 (1976).
[8]A. Vilenkin, Cosmic strings,and domain walls [J], Phys. Rep.121,263 (1985).
[9]M. Barriola and A. Vilenkin, Gravitational Field of a Global Monopolc[J], Phys. Rev. Lett.63,341 (1989).
[10]S. Perlmutter et al., Measurements of Omega and Lambda from 42 High-Redshift Supernovae[J], ApJ 517,565 (1999).
[11]A. G. Riess ct al., Observational Evidence from Supernovac for an Accelerating Universe and a Cosmological Constant[J], AJ 116,1009 (1998).
[12]D. N. Spergel et al., First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations:Determination of Cosmological Parameters[J], ApJS 148,175 (2003).
[13]B. Ratra and P. E. J. Peebles, Cosmological consequences of a rolling homogeneous scalar field[J], Phys. Rev. D 37,3406 (1988).
[14]R. R. Caldwell, R. Dave, and P. J. Steinhardt, Cosmological Imprint of an Energy Component with General Equation of Statc[J], Phys. Rev. Lett.80,1582 (1998).
[15]R. R. Caldwell, A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state [J], Phys. Lett. B 545,23 (2002).
[16]B. Feng, X. L. Wang and X. M. Zhang, Dark Energy Constraints from the Cosmic Age and Supernova[J], Phys. Lett. B 607,35 (2005).
[17]B. Feng, M. Z. Li, Y. S. Piao and X. Zhang, Oscillating Quintom and the Recurrent Universe[J], Phys. Lett. B 634,101 (2006).
[18]G. Zhao, J. Xia, M. Li, B. Feng, X. Zhang, Perturbations of the Quintom Models of Dark Energy and the Effects on Observations[J], Phys. Rev. D 72,123515 (2005).
[19]R. H. Dicke, Eotvos Experiment and the Gravitational Red Shift [J], Am. J. Phys. 28,344 (1960).
[20]L. I. Schiff, Possible new experimental test of general relativity theory[J], Phys. Rev. Lett.4,215 (1960).
[21]D. K.Ross and L. I. Schiff, Analysis of the proposed planetary radar reflection experiment[J], Phys. Rev.141,1215 (1966).
[22]I. I. Shapiro, Testing general relativity with radar[J], Phys. Rev.141,1219 (1966).
[23]B. B. Godfrey, Mach's Principle, the Kerr Metric, and Black Holc Physics[J], Phys. Rev. D 1,2721 (1970).
[24]J. K. Chose and P. Kumar, Gravitational mass defect in general relativity [J], Phys. Rev. D 13,2736 (1976).
[25]D. C. Wilkins, Bound Geodesies in the Kerr Mctric[J], Phys. Rev. D 5,814 (1972).
[26]P. H. Hu and Y. J. Wang, Repulsive effects in steady axisymmetric fields[J], Chin. Phys.15,1120 (2006).
[27]Chen J H, Wang Y J Gravitational frequency-shift and deflection of light by Quintessence[J], Chin. Phys.16,3212 (2007).
[28]T. X. Gong, A. G. Li. and Y. J. Wang, Gravitational effect of centre mass with electric charge and a large number of magnetic monopolcs[J], Chin. Phys.14(4), 859 (2005).
[29]王永久, 荷电天体的引力质量亏损[J].湖南师范大学自然科学学报04,29(2001).
[30]X. J. Huang and Y. J. Wang Mass-Defect Effect in the Hellings-Nordtvedt Field[J], Chin. Phys. Lett.19(6),755 (2002).
[31]龚添喜、王永久, 球对称度规场中的质量亏损效应[J].湖南师范大学自然科学学报27(03),39(2004).
[32]T. X. Gong and Y. J. Wang, Mass defect effect in the gravitational field[J], Chin. Phys.14(1),45 (2005).
[33]王永久、唐智明,质量四极矩场中的轨道进动效应[J],50(12)2284(2001).
[34]T. X. Gong and Y. J. Wang, Orbital effect in the stationary axisymmetric field[J], Chin. Phys. B 17(7),2356 (2008).
[35]罗新炼、王永久、程立伟, 旋转荷电球体外部引力场中引力效应[J],物理学报46,846(1997).
[36]T. X. Gong and Y. J. Wang, Orbital Precession Effect in the Reissner-Nordstrom Field with a Global Monopole[J], Chin. Phys. Lett.26(3),030402 (2009).
[37]K. S. Virbhadra and G. F. R. Ellis, Schwarzschild black hole lensing[J], Phys. Rev. D 62,084003 (2000).
[38]K. Lake, Bending of light and the cosmological constant[J], Phys. Rev. D 65,087301 (2002).
[39]W. Rindler and M. Ishak, Contribution of the cosmological constant to the rela-tivistic bending of light revisited[J], Phys. Rev. D 76,043006 (2007).
[40]Y. Eriguchi and K. Nomoto, DOUBLE IMAGES OF THE SUPERNOVA 1987A BY THE GRAVITATIONAL LENS [J], Mod. Phys. Lett. A 2,645 (1987).
[41]龚添喜、王永久,一般稳态时空中光子的轨道效应[J].物理学报58,5988(2009).
[42]王永久、彭秋和,一种新型超巨质量(非黑洞)致密天体[J]，科学通报30(6),418(1985).
[43]刘辽、裴寿镛,量子史瓦茨黑洞和暗物质[J],物理学报55,4980(2006).
[44]王永久,经典黑洞和量子黑洞[M],北京：科学出版社(2008).
[45]Q. Y. Pan and J. L. Jing, Quasinormal modes of a stationary axisymmetric EMDA black hole[J], Chin. Phys.15,77 (2006).
[46]M. Sereno New interactions in the dark sector mediated by dark energy[J], Phys. Rev. D 77,043004 (2008).
[47]R. P. Kerr, Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics[J] Phys. Rev. Lett.11,237 (1963).
[48]E. T. Newman and A. I. Janis, Note on the Kerr spinning - particle metric[J] Math. Phys.6,344 (1965).
[49]M. Kasuya, Exact solution of a rotating dyon black hole[J], Phys. Rev. D 25,995 (1982).
[50]王永久,磁场中的旋转双荷黑洞[J]，物理学报33,1728(1984).
[51]P. A. M. Driac, Quantised Singularities in the Electromagnetic Field[J], Proc. Roy. Soc.133,60 (1931).
[52]Harish-Chandra, Motion of an Electron in the Field of a Magnetic Pole[J], Phys. Rev.74,883 (1948).
[53]Y. J. Wang and Q. H. Peng, GRAVITATIONAL PROPERTIES OF THE NEU-TRON STAR WITH MAGNETIC CHARGE AND MAGNETIC MOMENT [J], Sci. Sin.4,422 (1985).
[54]杨波, 一般加速带电带磁的动态黑洞中标量场的熵[J],物理学报55,2614(2008).
[55]C. J. Gao and Y. G. Shen, De Broglie-Bohm Quantization of the Reissner-Nordstrom Black Hole with a Global Monopole in the Background of de Sitter Space-Time[J], Chin. Phys. Lett.19(4),477 (2002).
[56]S. W. Hawking Gravitational radiation from colliding black holes[J], Phys. Rev. Lett.26,1344 (1971).
[57]R. Penrose Structure of space-time[M], ed. by C. M. Dewitt and J. A. Wheeler, Battelle Rencontres:1967 Lectures in Mathematics and Physics, New York:Ben-jamin (1968).
[58]J. D. Bekenstein, Black Holes and Entropy[J], Phys. Rev. D 3,2333 (1973).
[59]刘辽、赵峥,广义相对论[M],(第二版)北京：高等教育出版社, (2004).
[60]S. W. Hawking, Black hole explosions[J], Nature 248,30 (1974).
[61]S. W. Hawking, Particle creation by black holes[J], Commun. Math. Phys.43,199 (1975).
[62]S. W. Hawking, Breakdown of predictability in gravitational collapse[J], Phys. Rev. D 14,2460 (1976).
[63]J. B. Hartle and S. W. Hawking, Path-integral derivation of black-hole radiance[J], Phys. Rev. D 13 2188 (1976).
[64]W. Isreal Thermo-field dynamics of black hole[J], Phys. Lett. A 57,107 (1976).
[65]G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity[J], Phys. Rev. D 15,2752 (1977).
[66]L. Parker The production of elementary particles by strong gravitational fields[M], ed. by F. P. Esposito and L. Witten, New York:Plenum press, (1977).
[67]赵峥, 黑洞的热性质与时空奇异性---零曲面附近的量子效应[M],北京：北京师范大学出版社,(1999).
[68]刘辽、许殿彦,Dirac粒子的Hawking蒸发[J],物理学报29,1617(1980).
[69]T. Damoar and R. Ruffini, Black-hole evaporation in the Klein-Sauter-Heisenberg-Eulcr formalism [J], Phys. Rev. D 14,332 (1976).
[70]N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space [M], Cambridge: Cambridge University Press (1982).
[71]M. K. Parikh, Energy conservation and Hawking radiation [J], Gen. Rel. Grav.36, 2419 (2004).
[72]M. K. Parikh and F. Wilczek, Hawking radiation as tunneling[J], Phys. Rev. Lett. 85,5042 (2000).
[73]M. K. Parikh, A secret tunnel through the horizon[J], Int. J. Mod. Phys.13,2351 (2004).
[74]S. Hemming and E. Keski-Vakkuri, Hawking radiation from AdS black holes[J], Phys. Rev. D 64,044006 (2001).
[75]A. J. Medved, Radiation via tunneling from a de Sitter cosmological horizon[J], Phys. Rev. D 66,124009 (2002).
[76]M. K. Parikh, New coordinates for de Sitter space and de Sitter radiation[J], Phys. Lett. B 546,189 (2002).
[77]G. Q. Li, Dilaton black hole tunneling radiation in dc Sitter universe [J], Commun. Theor. Phys.51,453 (2009).
[78]J. Y. Zhang and Z. Zhao, New coordinates for Kerr- Newman black hole radia-tion[J], Phys. Lett. B 618 14 (2005).
[79]J. Y. Zhang and Z. Zhao, Hawking radiation of charged particle via tunneling form the Reissner-Nordstrom black holc[J], JHEP 10,055 (2005).
[80]L. Gao and W. B. Liu, General radiation via tunneling in Kerr and Kerr- Newman black holes[J] Sci. Chin. G 51,1200 (2008).
[81]S. Iso, H. Umctsu and F. Wilczek, Hawking radiation from charged black holes via gauge and gravitational anomalics[J] Phys. Rev. Lett.96,151302 (2006).
[82]Y. W. Han, Quantum non-thermal effect, from Kerr- Newman black hole[J], Com-mun. Thcor. Phys.51,450 (2009).
[83]P. M. Garnavich, et al, Supernova limits on the cosmic equation of state[J], Astro-phys. J 509,74 (1998).
[84]Y. J. Wang and Z. M. Tang, Gravitational properties of an accelerating celestial body with a large number of monopoles[J], Astrophys. and S. S.282,363 (2002).
[85]S. B. Chen, B. Wang and R. K. Su, Hawking radiation in a d-dimensional static spherically symmetric black hole surrounded by Quintessence[J], Phys. Rev. D 77, 124011 (2008).
[86]J. L. Jing and Y. J. Wang and J.Y. Zhu, Generalized first law of thermodynamics for black holes in spacetimes which are not asymptotically flat[J], Phys. Lett. A 18731 (1994).
[87]J. H. Chen and Y. J. Wang, Influence of dark energy on gravitational time delay[J], Commun. Theor. Phys.50,101 (2008).
[88]V. V. Kiselev, Quintessence and black holes[J], Class. Quantum Grav.20 1187 (2003).
[89]P. Painleve, The stationary coordinates in a Schwarzschild blck hole[J], C. R. Acad. Sci.(Paris) 173,677 (1921).
[90]E. C. Vagenas, Generalization of the KKW analysis for black hole radiation [J], Phys. Lett. B 559,65 (2003).
[91]P. Kraus and F. Wilczek, Self-interaction.correction to black hole radiance [J], Nucl. Phys. B 433,403 (1995).
[92]P. Kraus and F. Wilcze k, Effect of self-interaction on charged black hole radi-ance[J], Nucl. Phys. B 437,231 (1995).
[93]E. Keski-Vakkuri and P. Kraus, Tunneling in a time- dependent setting[J], Phys. Rev. D 54,7407 (1996).
[94]S. M. Christcnscn and S. A. Fulling, Trace anomalies and the Hawking effect[J], Phys. Rev. D 15 2088 (1977).
[95]赵峥, 四维静态黎曼时空中的Hawking辐射[J]，物理学报30 1508(1981).
[96]杨波、赵峥,一般球对称动态时空中荷电Dirac粒子的Hawking辐射[J],物理学报43,858(1994).
[97]M. R. Setare and E. C. Vagenas, Self-gravitational corrections to the Cardy-Verlinde formula of the Achucarro-Ortiz black hole [J], Phys. Lett. B 584 127 (2004).
[98]A. J. Medved, Radiation via tunnelling in the charged BTZ black hole [J], Class. Quant. Grav.19,589 (2002).
[99]A. J. Medved and E. C. Vagenas, ON HAWKING RADIATION AS TUNNELING WITH BACK-REACTION [J], Mod. Phys. Lett. A 20,2449 (2005).
[100]M. Arzano, A. J. Medved and E. C. Vagenas, Hawking Radiation as Tunneling through the Quantum Horizon [J], JHEP 0509,037 (2005).
[101]M. R. Setare and E. C. Vagenas, Area Spectrum of Kerr and extremal Kerr Black Holes from Quasinormal Modes [J], Mod. Phys. Lett. A 20,1923 (2005).
[102]R. Kerner and R. B. Mann, Tunnelling, temperature, and Taub-NUT black holes[J], Phys. Rev. D 73,104010 (2006).
[103]J. Y. Zhang and Z. Zhao, New coordinates for Kerr-Newman black hole radiation [J], Phys. Lett. B 618,14 (2005).
[104]韩亦文,用量子隧穿法研究带质量四极矩静态黑洞的Hawking辐射[J]，物理学报54,5018(2005).
[105]胡亚鹏、张靖仪、.赵峥,Reissner-Nordstrom黑洞中带电粒子由隧穿导致的Hawking辐射的进一步讨论[J],物理学报56 0683(2007).
[106]Q. Q. Jing, S. Q. Wu and X. Cai, Hawking radiation from dilatonic black holes via anomalies [J], Phys. Rev. D 75,064029 (2007).
[107]R. Kerner and R. B. Mann, Tunnclling from Godcl black holes[J], Phys. Rev. D 75,084022 (2007).
[108]R. Li and J. R. Ren, Dirac particles tunneling from BTZ black hole [J], Phys. Lett. B 661 370 (2008).
[109]J. J. Peng and S. Q. Wu, Covariant anomalies and Hawking radiation from charged rotating black strings in anti-de Sitter spacetimes [J], Phys. Lett. B 661,300 (2008).
[110]R. Kerner and R. B. Mann, Charged fermions tunnelling from Kerr-Newman black holes [J], Phys. Lett. B 665 277 (2008).
[111]S. Das, P. Majumdar and R. K. Bhaduri, Absence of higher derivatives in the renormalization of propagators in quantum field theories with infinitely many cou-plings [J], Class. Quantum Grav.20,2355 (2002).
[112]Q. Q. Jing, Fermions tunnelling from GHS and non-extremal D1-D5 black holes [J], Phys. Lett. B 666,517 (2008).
[113]Z. Z. Ma, Hawking temperature of Kerr-Newman-AdS black hole from tunneling [J], Phys. Lett. B 666,376 (2008).
[114]B. Zhang, Q. Y. Cai and M. S. Zhan, Hawking radiation as tunneling derived from black hole thermodynamics through the quantum horizon [J], Phys. Lett. B 665, 260 (2008).
[115]X. K. He and W. B. Liu, Modified Hawking radiation in a BTZ black hole using Damour-Ruffini method [J], Phys. Lett. B 653,330 (2007).
[116]S. W. Zhou and W. B. Liu, Hawking radiation of charged Dirac particles from a Kerr-Newman black hole[J], Phys. Rev. D 77,104021 (2008).
[117]J. Y. Zhang, Black hole quantum tunnelling and black hole entropy correction [J], Phys. Lett. B 668,353 (2008).
[118]J. Y. Zhang and J. H. Fanm Hawking radiation via tunnelling from general sta-tionary axisymmetric black holes[J], Chin. Phys. B 16,3879 (2007).
[119]张靖仪、赵峥,电磁直线加速动态黑洞时空中Dirac粒子的Hawking辐射[J],物理学报52,2096(2003).
[120]刘文彪,Damour-Ruffini方法和Rcissncr-Nordstrom黑洞的非热Hawking辐射[J]，物理学报56,6164(2007).
[121]T. X. Gong and Y. J. Wang Quantum Non-thermal Effect from Black Holes Surrounded by Quintessence[J], Commun. Theor. Phys.52,974 (2009).
[122]D. V. Fursaev, Temperature and entropy of a quantum black hole and conformal anomaly[J], Phys. Rev. D 51, R5352 (1995).
[123]R. B. Mann and S. N. Solodukhin, Universality of Quantum Entropy for Extreme Black Holes [J], Nucl. Phys. B 523,293 (1998)
[124]R. K. Kaul and P. Majumdar, Logarithmic Correction to the Bekenstein-Hawking Entropy[J], Phys. Rev. Lett.84,5255 (2000).
[125]T. R. Govindarajan, R. K. Kaul and V. Suneeta, Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole[J], Class. Quantum Grav.18, 2877 (2001).
[126]S. S. More, Higher order corrections to black hole entropy[J], Class. Quantum Grav.22,4129 (2005).
[127]S. Mukherji and S. S. Pal, Logarithmic Corrections to Black Hole Entropy and AdS/CFT Correspondence [J], JHEP 0205,026 (2002).
[128]A. Ghosh and P. Mitra, An improved estimate of black hole entropy in the quantum geometry approach [J], Phys. Lett. B 616,114 (2005).
[129]D. N. Page, Hawking Radiation and Black Hole Thermodynamics[J], New Journal of Phys.7,203 (2005).
[130]R. Banerjee and B. R. Majhi, Quantum Tunneling Beyond Semiclassical Approx-imation [J], JHEP 0806,095 (2008).
[131]K Srinivasan and T Padmanabhan, Particle production and complex path analy-sis[J], Phys. Rev. D 60,024007 (1999).
[132]S K Modak, Corrected entropy of BTZ black hole in tunneling approach [J], Phys. Lett. B 671,167 (2009).
[133]P Mitra, Hawking temperature from tunnelling formalism [J], Phys. Lett. B 648, 240 (2007)
[134]J W York Jr, Black hole in thermal equilibrium with a scalar field:The back-reaction[J], Phys. Rev. D 31,775 (1985).
[135]C. O. Lousto and N. Sanchez, Back reaction effects in black hole spacetimes [J], Phys. Lett. B 212,411 (1988).
[136]J. M. Bardeen, B. Carter and S. W. Hawking, The four laws of black hole mechanics [J], Commun. Thcor. Phys.,31,161 (1973).