5维黑洞背景下费米子的霍金辐射
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摘要
本文基于量子反常抵消方法,有效作用量方法,Damour-Ruffini-Sannan(DRS)方法以及密度矩阵技术研究了五维Godel黑洞和五维Myers-Perry黑洞Dirac粒子的Hawking辐射和Hawking黑体谱。
利用维度约化技术,我们发现五维Godel黑洞和五维Myers-Perry黑洞中的费米场可以由(1+1)维背景时空下的二分量量子场和Dilaton场与U(1)规范场的耦合所描述。在这个有效两维的量子场中,因为所有入的模式不能影响到视界面外部的物理效应,在规范和一般坐标对称性条件下,外部的有效二维作用量体现出了奇异性。为了抵消奇异反常,Hawking通量就变成了视界面上的反常荷。从而得到了Hawking温度和Hawking通量。
在有效作用量基础上,通过取协变的边界条件,协变的规范通流以及协变能动张量,由迹反常也可以正确的推导出Hawking通量。这种方法非常的直接和有效,因为通量和能动张量的表达可直接通过对有效作用量的函数微分获得。
为了形成对照,我们还通过DRS方法计算了黑洞的Hawking温度。而这三种方法所得到的Hawking温度都和表面引力机制相一致。量子反常抵消取消方法和有效作用量方法所得到的Hawking通量也和Planck分布一致。
最后,我们通过密度矩阵技术得到了五维Godel黑洞和五维Myers-Perry黑洞的Hawking辐射谱。结果表明,辐射光谱在Hawking温度下是一个完美的黑体辐射谱。
In this thesis, we apply the quantum anomaly cancellation method andthe effective action approach as well as the method ofDamour-Ruffini-Sannan(DRS) to derive Hawking radiation of Dirac particles from five dimensional Godel and Myers-Perry black hole. We also investigate the Hawking black body spectrum of these black holes by using density matrix techniques.
Using the dimensional reduction technique, we find that the fermionic field in the back-ground of the Godel and Myers-Perry black hole can be treated as an infinite collection of quantum fields in (1+1)-dimensional background coupled with the dilaton field and the U(1) gauge field near the horizon. In this two-dimensional reduction, as all the ingoing modes can not classically affect physics outside the horizon, the two-dimensional effective action in the exterior region becomes anomalous with respect to gauge or general coordinate symmetries. To cancel the anomaly, the Hawking flux is universally determined only by the value of anomalies at the horizon. Thus Hawking temperature and fluxes are found.
Another method to correctly reproduce Hawking fluxes is based on the effective action which is induced from trace anomaly by using the covariant boundary condition and the co-variant gauge current as well as the covariant energy-momentum tensor. This approach is particularly direct and useful since one is able to obtain an expression for the currents and energy-momentum tensors directly by taking appropriate functional derivatives of the effective action.
By comparison, we also calculate the Hawking temperature via the method of Damour-Ruffini-Sannan. The Hawking temperature obtained agrees with the surface gravity formula while the Hawking fluxes derived from the anomaly cancellation method and the effective ac-tion approach are in complete agreement with the ones obtained from integrating the Planck distribution.
Finally, using density matrix techniques, we obtain the Hawking radiation spectrum of the Godel and Myers-Perry black hole. It is shown that the radiation spectrum is consistent with a perfect blackbody spectrum in the Hawking temperature.
利用维度约化技术,我们发现五维Godel黑洞和五维Myers-Perry黑洞中的费米场可以由(1+1)维背景时空下的二分量量子场和Dilaton场与U(1)规范场的耦合所描述。在这个有效两维的量子场中,因为所有入的模式不能影响到视界面外部的物理效应,在规范和一般坐标对称性条件下,外部的有效二维作用量体现出了奇异性。为了抵消奇异反常,Hawking通量就变成了视界面上的反常荷。从而得到了Hawking温度和Hawking通量。
在有效作用量基础上,通过取协变的边界条件,协变的规范通流以及协变能动张量,由迹反常也可以正确的推导出Hawking通量。这种方法非常的直接和有效,因为通量和能动张量的表达可直接通过对有效作用量的函数微分获得。
为了形成对照,我们还通过DRS方法计算了黑洞的Hawking温度。而这三种方法所得到的Hawking温度都和表面引力机制相一致。量子反常抵消取消方法和有效作用量方法所得到的Hawking通量也和Planck分布一致。
最后,我们通过密度矩阵技术得到了五维Godel黑洞和五维Myers-Perry黑洞的Hawking辐射谱。结果表明,辐射光谱在Hawking温度下是一个完美的黑体辐射谱。
In this thesis, we apply the quantum anomaly cancellation method andthe effective action approach as well as the method ofDamour-Ruffini-Sannan(DRS) to derive Hawking radiation of Dirac particles from five dimensional Godel and Myers-Perry black hole. We also investigate the Hawking black body spectrum of these black holes by using density matrix techniques.
Using the dimensional reduction technique, we find that the fermionic field in the back-ground of the Godel and Myers-Perry black hole can be treated as an infinite collection of quantum fields in (1+1)-dimensional background coupled with the dilaton field and the U(1) gauge field near the horizon. In this two-dimensional reduction, as all the ingoing modes can not classically affect physics outside the horizon, the two-dimensional effective action in the exterior region becomes anomalous with respect to gauge or general coordinate symmetries. To cancel the anomaly, the Hawking flux is universally determined only by the value of anomalies at the horizon. Thus Hawking temperature and fluxes are found.
Another method to correctly reproduce Hawking fluxes is based on the effective action which is induced from trace anomaly by using the covariant boundary condition and the co-variant gauge current as well as the covariant energy-momentum tensor. This approach is particularly direct and useful since one is able to obtain an expression for the currents and energy-momentum tensors directly by taking appropriate functional derivatives of the effective action.
By comparison, we also calculate the Hawking temperature via the method of Damour-Ruffini-Sannan. The Hawking temperature obtained agrees with the surface gravity formula while the Hawking fluxes derived from the anomaly cancellation method and the effective ac-tion approach are in complete agreement with the ones obtained from integrating the Planck distribution.
Finally, using density matrix techniques, we obtain the Hawking radiation spectrum of the Godel and Myers-Perry black hole. It is shown that the radiation spectrum is consistent with a perfect blackbody spectrum in the Hawking temperature.
引文
[1]P. C. W. Davies, Thermodynamics of black holes, Rep. Prog. Phys. (1978),41(8):1313-1355.
[2]S. W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. (1975),43(3):199-220.
[3]S. W. Hawking, Black hole explosions? Nature. (1974),248:30-31.
[4]J. D. Bekenstein, Black Holes and Entropy, Phys. Rev. D (1973),7(8):2333-2346.
[5]L. Smarr, Mass Formula for Kerr Black Holes, Phys. Rev. Lett. (1973),30(2):71-73.
[6]王永久,经典黑洞和量子黑洞,北京：科学出版社,(2008),ISBN：978-7-03-022539-9.
[7]赵峥,黑洞与弯曲的时空,太原：山西科学技术出版社,(2001),ISBN：7-5377-1652-8.
[8]刘辽,赵峥,田贵花,张靖仪,黑洞与时间的性质,北京：北京大学出版社,(2008),ISBN：978-7-301-14675-0.
[9]T. Damour and R. Ruffini, Black-hole evaporation in the Klein-Sauter-Heisenberg-Euler formalism, Phys. Rew. D (1976),14(2):332-334.
[10]S. Christensen and S. Fulling, Trace anomalies and the Hawking effect, Phys. Rev. D (1977), 15(8):2088-2104.
[11]M. K. Parikh and F. Wilczek, Hawking Radiation As Tunneling, Phys. Rev. Lett. (2000), 85(24):5042-5045.
[12]K. Srinivasan and T. Padmanabhan, Particle production and complex path analysis, Phys. Rev. D (1999),60(2):024007.
[13]S. Shankaranarayanan, T. Padmanabhan, and K. Srinivasan, Hawking radiation in different coordi-nate settings:complex paths approach, Class. Quant. Grav. (2002),19(10):2671-2688.
[14]M. Angheben, M. Nadalini, L. Vanzo, and S. Zerbini, Hawking radiation as tunneling for extremal and rotating black holes, JHEP (2005),0505:014.
[15]M. Nadalini, L. Vanzo, and S. Zerbini, Hawking radiation as tunnelling:the D-dimensional rotating case, J. Phys. A:Math. Gen. (2006),39(21):6601-6608.
[16]S. P. Robinson and F. Wilczek, Relationship between Hawking Radiation and Gravitational Anoma-lies, Phys. Rev. Lett. (2005),95(1):011303.
[17]S. Iso, H. Umetsu, and F. Wilczek, Hawking Radiation from Charged Black Holes via Gauge and Gravitational Anomalies, Phys. Rev. Lett. (2006),96(15):151302.
[18]S. Iso, H. Umetsu, and F. Wilczek, Anomalies, Hawking radiations, and regularity in rotating black holes, Phys. Rev. D (2006),74(4):044017.
[19]K. Murata and J. Soda, Hawking radiation from rotating black holes and gravitational anomalies, Phys. Rev. D (2006),74(4):044018.
[20]M. R. Setare, Gauge and Gravitational Anomalies and Hawking Radiation of Rotating BTZ Black Holes, Eur. Phys. J. C (2007),49(3):865-868.
[21]S. Iso, T. Morita, and H. Umetsu, Quantum anomalies at horizon and Hawking radiations in Myers-Perry black holes, JHEP (2007),0704:068.
[22]Q. Q. Jiang and S. Q. Wu, Hawking radiation from rotating black holes in anti-de Sitter spaces via gauge and gravitational anomalies, Phys. Lett. B (2007),647(2-3):200-206.
[23]Q. Q. Jiang, S. Q. Wu, and Xu Cai, Hawking radiation from dilatonic black holes via anomalies, Phys. Rev. D (2007),75(6):064029.
[24]K. Xiao, W. B. Liu, and H. B. Zhang, Anomalies of the Achucarro-Ortiz black hole, Phys. Lett. B (2007),647(5-6):482-485.
[25]H. Shin and W. Kim, Hawking radiation from non-extremal D1-D5 black hole via anomalies, JHEP (2007),0706:012.
[26]Q. Q. Jiang, S. Q. Wu, and X. Cai, Anomalies and de Sitter radiation from the generic black holes in de Sitter spaces, Phys. Lett. B (2007),651(1):65-70.
[27]S. Q. Wu and J. J. Peng, Anomalies and Hawking radiation from the Reissner-Nordstrom black hole with a global monopole, Class. Quant. Grav. (2007),24(20):5123-5138.
[28]W. Kim and H. Shin, Anomaly analysis of Hawking radiation from acoustic black hole, JHEP (2007),0707:070.
[29]K. Murata and U. Miyamoto, Hawking radiation of a vector field and gravitational anomalies, Phys. Rev. D (2007),76(8):084038.
[30]R. Banerjee and S. Kulkarni, Hawking radiation and covariant anomalies, Phys. Rev. D (2008), 77(2):024018.
[31]R. Banerjee and S. Kulkarni, Hawking radiation, effective actions and covariant boundary condi-tions, Phys. Lett. B (2008),659(4):827-831.
[32]Q. Q. Jiang and X. Cai, Covariant anomalies, effective action and Hawking radiation from Kerr-Godel black hole, Phys. Lett. B (2009),677(3-4):179-185.
[33]R. Banerjee, S. Gangopadhyay, and S. Kulkarni, Hawking radiation and near horizon universality of chiral Virasoro algebra, (2008), arXiv:0804.3492.
[34]R. Banerjee, COVARIANT ANOMALIES, HORIZONS AND HAWKING RADIATION, Int. J. Mod. Phys. D (2009),17(3-4):2539-2542.
[35]R. Banerjee and S. Kulkarni, Hawking radiation, covariant boundary conditions, and vacuum states, Phys. Rev. D (2009),79(8):084035.
[36]S. Gangopadhyay and S. Kulkarni, Hawking radiation from Garfinkle-Horowitz-Strominger and nonextremal D1-D5 black holes via covariant anomalies, Phys. Rev. D (2008),77(2):024038.
[37]J. J. Peng and S. Q. Wu, Covariant anomalies and Hawking radiation from charged rotating black strings in anti-de Sitter spacetimes, Phys. Lett. B (2008),661(4):300-306.
[38]X. N. Wu, C. G. Huang, and J. R. Sun, Gravitational anomaly and Hawking radiation near a weakly isolated horizon, Phys. Rev. D (2008),77(12):124023.
[39]S. Q. Wu, J. J. Peng, and Z. Y. Zhao, Anomalies, effective action and Hawking temperatures of a Schwarzschild black hole in the isotropic coordinates, Class. Quant. Grav. (2008),25(13):135001.
[40]S. Gangopadhyay, Hawking radiation from a Reissner-Nordstrom black hole with a global monopole via covariant anomalies and effective action, Phys. Rev.D (2008),78(4):044026.
[41]S. Gangopadhyay, Anomalies, horizons and Hawking radiation, Europhys. Lett. (2009), 85(1):10004.
[42]E. Papantonopoulos and P. Skamagoulis, Hawking radiation via gravitational anomalies in non-spherical topologies, Phys. Rev. D (2009),79(8):084022.
[43]R. Li, J. R. Ren, and S. W. Wei, Gravitational anomaly and Hawking radiation of apparent horizon in FRW universe, Eur. Phys. J. C (2009),62(3):455-458.
[44]S. W. Wei, R. Li, Y. X. Liu, and J. R. Ren, Anomaly analysis of Hawking radiation from Kaluza-Klein black hole with squashed horizon, Eur. Phys. J. C (2010),281-287.
[45]S. Nam and J. D. Park, Hawking radiation from covariant anomalies in (2+1)-dimensional black holes, Class. Quant. Grav. (2009),26(14):145015.
[46]T. Morita, Modification of gravitational anomaly method in Hawking radiation, Phys. Lett. B (2009),677(1-2):88-92.
[47]A. P. Porfyriadis, Hawking radiation via anomaly cancellation for the black holes of five-dimensional minimal gauged supergravity, Phys. Rev. D (2009),79(8):084039.
[48]A. P. Porfyriadis, Anomalies and Hawking fluxes from the black holes of topologically massive gravity, Phys. Lett. B (2009),675(2):235-239.
[49]S. W. Wei, R. Li, Y. X. Liu, and J. R. Ren, Anomaly analysis of Hawking radiation from 2+1 dimensional spinning black hole, (2009), arXiv:0904.2915.
[50]S. Iso, T. Morita, and H. Umetsu, Higher-spin currents and thermal flux from Hawking radiation, Phys. Rev. D (2007),75(12):124004.
[51]S. Iso, T. Morita, and H. Umetsu, Fluxes of higher-spin currents and Hawking radiation from charged black holes, Phys. Rev. D (2007),76(6):064015.
[52]S. Iso, T. Morita, and H. Umetsu, Hawking radiation via higher-spin gauge anomalies, Phys. Rev. D (2008),77(4):045007.
[53]S. Iso, T. Morita, and H. Umetsu, Higher-spin gauge and trace anomalies in two-dimensional back-grounds, Nucl. Phys. B (2008),799(1-2)60-79.
[54]S. Iso, HAWKING RADIATION, GRAVITATIONAL ANOMALY, AND CONFORMAL SYMMETRY—THE ORIGIN OF UNIVERSALITY, Int. J. Mod. Phys. A (2008),23(14-15):2082-2090.
[55]L. Bonora and M. Cvitan, Hawking radiation, W∞ algebra and trace anomalies, JHEP (2008), 0805:071.
[56]L.Bonora, M.Cvitan, S.Pallua, and I.Smolic, Hawking fluxes, W∞ algebra and anomalies, JHEP (2008),0812:021.
[57]L. Bonora, M. Cvitan, S. Pallua, and I. Smolic, Hawking fluxes, fermionic currents, W1+∞ algebra, and anomalies, Phys. Rev. D (2009),80(8):084034.
[58]T. Morita, Hawking radiation and quantum anomaly in AdS2/CFT1 correspondence, JHEP (2009), 0901:037.
[59]S. Ghosh, Combining The Tunneling And Anomaly Phenomena In Deriving the Gravitational Anomaly, (2008), arXiv:0804.2999.
[60]V. Akhmedova, T. Pilling, A. Gill, and D. Singleton, Comments on anomaly versus WKB/tunneling methods for calculating Unruh radiation, Phys. Lett. B (2009),673(3):227-231.
[61]R. Banerjee and B. R. Majhi, Connecting anomaly and tunneling methods for the Hawking effect through chirality, Phys. Rev. D (2009),79(6):064024.
[62]R. Banerjee and B. R. Majhi, Quantum tunneling and trace anomaly, Phys. Lett. B (2009), 674(3):218-222.
[63]A. M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B (1981),103(3):207-210.
[64]V. Mukhanov, A. Wipf, and A. Zelnikov, On 4D Hawking radiation from the effective action, Phys. Lett. B (1994),332(3-4):283-291.
[65]V. P. Frolov, W. Israel, and S. N. Solodukhin, One-loop quantum corrections to the thermodynamics of charged black holes, Phys. Rev. D (1996),54(4):2732-2745.
[66]M. Buric, V. Radovanovic, and A. Mikovic, One-loop corrections for a Schwarzschild black hole via 2D dilaton gravity, Phys. Rev. D (1999),59(8):084002.
[67]F. C. Lombardo, F. D. Mazzitelli, and J. G. Russo, Energy-momentum tensor for scalar fields cou-pled to the dilaton in two dimensions, Phys. Rev. D (1999),59(6):064007.
[68]S. Nojiri and S. D. Odintsov, Trace-anomaly-induced effective action for 2D and 4D dilaton coupled scalars, Phys. Rev. D (1998),57(4):2363-2371.
[69]W. Kummer and D. V. Vassilevich, Hawking radiation from dilaton gravity in 1+1 dimensions:a pedagogical review, Ann. Phys. (Leipzig) (1999),8(10):801-827.
[70]R. Balbinot and A. Fabbri, Two-dimensional black holes and effective actions, Class. Quantum. Grav. (2003),20(24):5439-5454.
[71]R. Balbinot and A. Fabbri, Hawking radiation by effective two-dimensional theories, Phys. Rev. D (1999),59(4):044031.
[72]R. Balbinot and A. Fabbri,4D quantum black hole physics from 2D models? Phys. Lett. B (1999), 459(1-3):112-118.
[73]R. Balbinot, A. Fabbri, and I. Shapiro, Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions, Nucl. Phys. B (1999),559(1-2):301-319.
[74]S. Gangopadhyay, Hawking radiation from the Garfinkle-Horowitz-Strominger black hole, effective action, and covariant boundary condition, Phys. Rev. D (2008),77(6):064027.
[75]S. Kulkarni, Hawking fluxes, back reaction and covariant anomalies, Class. Quant. Grav. (2008), 25(22):225023.
[76]R. Banerjee and B.R. Majhi, Hawking black body spectrum from tunneling mechanism, Phys. Lett. B (2009),675(2):243-245.
[77]S. Q. Wu, General Nonextremal Rotating Charged Godel Black Holes in Minimal Five-Dimensional Gauged Supergravity, Phys. Rev. Lett. (2008),100(12):121301.
[78]R. C. Myers and M. J. Perry, Black holes in higher dimensional space-times, Ann. Phys. (N.Y.) (1986),172(2):304-347.
[79]S. Q. Wu, Separability of the massive Dirac equation in 5-dimensional Myers-Perry black hole geometry and its relation to a rank-three Killing-Yano tensor, Phys. Rev. D (2008),78(6):064052.
[80]J. Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity, Adv. Theor. Math. Phys. (1998),2(2):231-252.
[81]S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B (1998),428(1-2):105.
[82]E. Witten, Anti de Sitter Space and Holography, Adv. Theor. Math. Phys. (1998),2(2):253-290.
[83]O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. (2000),323(3-4):183-386.
[84]A. Strominger, Black hole entropy from near-horizon microstates, JHEP (1998),9802:009.
[2]S. W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. (1975),43(3):199-220.
[3]S. W. Hawking, Black hole explosions? Nature. (1974),248:30-31.
[4]J. D. Bekenstein, Black Holes and Entropy, Phys. Rev. D (1973),7(8):2333-2346.
[5]L. Smarr, Mass Formula for Kerr Black Holes, Phys. Rev. Lett. (1973),30(2):71-73.
[6]王永久,经典黑洞和量子黑洞,北京：科学出版社,(2008),ISBN：978-7-03-022539-9.
[7]赵峥,黑洞与弯曲的时空,太原：山西科学技术出版社,(2001),ISBN：7-5377-1652-8.
[8]刘辽,赵峥,田贵花,张靖仪,黑洞与时间的性质,北京：北京大学出版社,(2008),ISBN：978-7-301-14675-0.
[9]T. Damour and R. Ruffini, Black-hole evaporation in the Klein-Sauter-Heisenberg-Euler formalism, Phys. Rew. D (1976),14(2):332-334.
[10]S. Christensen and S. Fulling, Trace anomalies and the Hawking effect, Phys. Rev. D (1977), 15(8):2088-2104.
[11]M. K. Parikh and F. Wilczek, Hawking Radiation As Tunneling, Phys. Rev. Lett. (2000), 85(24):5042-5045.
[12]K. Srinivasan and T. Padmanabhan, Particle production and complex path analysis, Phys. Rev. D (1999),60(2):024007.
[13]S. Shankaranarayanan, T. Padmanabhan, and K. Srinivasan, Hawking radiation in different coordi-nate settings:complex paths approach, Class. Quant. Grav. (2002),19(10):2671-2688.
[14]M. Angheben, M. Nadalini, L. Vanzo, and S. Zerbini, Hawking radiation as tunneling for extremal and rotating black holes, JHEP (2005),0505:014.
[15]M. Nadalini, L. Vanzo, and S. Zerbini, Hawking radiation as tunnelling:the D-dimensional rotating case, J. Phys. A:Math. Gen. (2006),39(21):6601-6608.
[16]S. P. Robinson and F. Wilczek, Relationship between Hawking Radiation and Gravitational Anoma-lies, Phys. Rev. Lett. (2005),95(1):011303.
[17]S. Iso, H. Umetsu, and F. Wilczek, Hawking Radiation from Charged Black Holes via Gauge and Gravitational Anomalies, Phys. Rev. Lett. (2006),96(15):151302.
[18]S. Iso, H. Umetsu, and F. Wilczek, Anomalies, Hawking radiations, and regularity in rotating black holes, Phys. Rev. D (2006),74(4):044017.
[19]K. Murata and J. Soda, Hawking radiation from rotating black holes and gravitational anomalies, Phys. Rev. D (2006),74(4):044018.
[20]M. R. Setare, Gauge and Gravitational Anomalies and Hawking Radiation of Rotating BTZ Black Holes, Eur. Phys. J. C (2007),49(3):865-868.
[21]S. Iso, T. Morita, and H. Umetsu, Quantum anomalies at horizon and Hawking radiations in Myers-Perry black holes, JHEP (2007),0704:068.
[22]Q. Q. Jiang and S. Q. Wu, Hawking radiation from rotating black holes in anti-de Sitter spaces via gauge and gravitational anomalies, Phys. Lett. B (2007),647(2-3):200-206.
[23]Q. Q. Jiang, S. Q. Wu, and Xu Cai, Hawking radiation from dilatonic black holes via anomalies, Phys. Rev. D (2007),75(6):064029.
[24]K. Xiao, W. B. Liu, and H. B. Zhang, Anomalies of the Achucarro-Ortiz black hole, Phys. Lett. B (2007),647(5-6):482-485.
[25]H. Shin and W. Kim, Hawking radiation from non-extremal D1-D5 black hole via anomalies, JHEP (2007),0706:012.
[26]Q. Q. Jiang, S. Q. Wu, and X. Cai, Anomalies and de Sitter radiation from the generic black holes in de Sitter spaces, Phys. Lett. B (2007),651(1):65-70.
[27]S. Q. Wu and J. J. Peng, Anomalies and Hawking radiation from the Reissner-Nordstrom black hole with a global monopole, Class. Quant. Grav. (2007),24(20):5123-5138.
[28]W. Kim and H. Shin, Anomaly analysis of Hawking radiation from acoustic black hole, JHEP (2007),0707:070.
[29]K. Murata and U. Miyamoto, Hawking radiation of a vector field and gravitational anomalies, Phys. Rev. D (2007),76(8):084038.
[30]R. Banerjee and S. Kulkarni, Hawking radiation and covariant anomalies, Phys. Rev. D (2008), 77(2):024018.
[31]R. Banerjee and S. Kulkarni, Hawking radiation, effective actions and covariant boundary condi-tions, Phys. Lett. B (2008),659(4):827-831.
[32]Q. Q. Jiang and X. Cai, Covariant anomalies, effective action and Hawking radiation from Kerr-Godel black hole, Phys. Lett. B (2009),677(3-4):179-185.
[33]R. Banerjee, S. Gangopadhyay, and S. Kulkarni, Hawking radiation and near horizon universality of chiral Virasoro algebra, (2008), arXiv:0804.3492.
[34]R. Banerjee, COVARIANT ANOMALIES, HORIZONS AND HAWKING RADIATION, Int. J. Mod. Phys. D (2009),17(3-4):2539-2542.
[35]R. Banerjee and S. Kulkarni, Hawking radiation, covariant boundary conditions, and vacuum states, Phys. Rev. D (2009),79(8):084035.
[36]S. Gangopadhyay and S. Kulkarni, Hawking radiation from Garfinkle-Horowitz-Strominger and nonextremal D1-D5 black holes via covariant anomalies, Phys. Rev. D (2008),77(2):024038.
[37]J. J. Peng and S. Q. Wu, Covariant anomalies and Hawking radiation from charged rotating black strings in anti-de Sitter spacetimes, Phys. Lett. B (2008),661(4):300-306.
[38]X. N. Wu, C. G. Huang, and J. R. Sun, Gravitational anomaly and Hawking radiation near a weakly isolated horizon, Phys. Rev. D (2008),77(12):124023.
[39]S. Q. Wu, J. J. Peng, and Z. Y. Zhao, Anomalies, effective action and Hawking temperatures of a Schwarzschild black hole in the isotropic coordinates, Class. Quant. Grav. (2008),25(13):135001.
[40]S. Gangopadhyay, Hawking radiation from a Reissner-Nordstrom black hole with a global monopole via covariant anomalies and effective action, Phys. Rev.D (2008),78(4):044026.
[41]S. Gangopadhyay, Anomalies, horizons and Hawking radiation, Europhys. Lett. (2009), 85(1):10004.
[42]E. Papantonopoulos and P. Skamagoulis, Hawking radiation via gravitational anomalies in non-spherical topologies, Phys. Rev. D (2009),79(8):084022.
[43]R. Li, J. R. Ren, and S. W. Wei, Gravitational anomaly and Hawking radiation of apparent horizon in FRW universe, Eur. Phys. J. C (2009),62(3):455-458.
[44]S. W. Wei, R. Li, Y. X. Liu, and J. R. Ren, Anomaly analysis of Hawking radiation from Kaluza-Klein black hole with squashed horizon, Eur. Phys. J. C (2010),281-287.
[45]S. Nam and J. D. Park, Hawking radiation from covariant anomalies in (2+1)-dimensional black holes, Class. Quant. Grav. (2009),26(14):145015.
[46]T. Morita, Modification of gravitational anomaly method in Hawking radiation, Phys. Lett. B (2009),677(1-2):88-92.
[47]A. P. Porfyriadis, Hawking radiation via anomaly cancellation for the black holes of five-dimensional minimal gauged supergravity, Phys. Rev. D (2009),79(8):084039.
[48]A. P. Porfyriadis, Anomalies and Hawking fluxes from the black holes of topologically massive gravity, Phys. Lett. B (2009),675(2):235-239.
[49]S. W. Wei, R. Li, Y. X. Liu, and J. R. Ren, Anomaly analysis of Hawking radiation from 2+1 dimensional spinning black hole, (2009), arXiv:0904.2915.
[50]S. Iso, T. Morita, and H. Umetsu, Higher-spin currents and thermal flux from Hawking radiation, Phys. Rev. D (2007),75(12):124004.
[51]S. Iso, T. Morita, and H. Umetsu, Fluxes of higher-spin currents and Hawking radiation from charged black holes, Phys. Rev. D (2007),76(6):064015.
[52]S. Iso, T. Morita, and H. Umetsu, Hawking radiation via higher-spin gauge anomalies, Phys. Rev. D (2008),77(4):045007.
[53]S. Iso, T. Morita, and H. Umetsu, Higher-spin gauge and trace anomalies in two-dimensional back-grounds, Nucl. Phys. B (2008),799(1-2)60-79.
[54]S. Iso, HAWKING RADIATION, GRAVITATIONAL ANOMALY, AND CONFORMAL SYMMETRY—THE ORIGIN OF UNIVERSALITY, Int. J. Mod. Phys. A (2008),23(14-15):2082-2090.
[55]L. Bonora and M. Cvitan, Hawking radiation, W∞ algebra and trace anomalies, JHEP (2008), 0805:071.
[56]L.Bonora, M.Cvitan, S.Pallua, and I.Smolic, Hawking fluxes, W∞ algebra and anomalies, JHEP (2008),0812:021.
[57]L. Bonora, M. Cvitan, S. Pallua, and I. Smolic, Hawking fluxes, fermionic currents, W1+∞ algebra, and anomalies, Phys. Rev. D (2009),80(8):084034.
[58]T. Morita, Hawking radiation and quantum anomaly in AdS2/CFT1 correspondence, JHEP (2009), 0901:037.
[59]S. Ghosh, Combining The Tunneling And Anomaly Phenomena In Deriving the Gravitational Anomaly, (2008), arXiv:0804.2999.
[60]V. Akhmedova, T. Pilling, A. Gill, and D. Singleton, Comments on anomaly versus WKB/tunneling methods for calculating Unruh radiation, Phys. Lett. B (2009),673(3):227-231.
[61]R. Banerjee and B. R. Majhi, Connecting anomaly and tunneling methods for the Hawking effect through chirality, Phys. Rev. D (2009),79(6):064024.
[62]R. Banerjee and B. R. Majhi, Quantum tunneling and trace anomaly, Phys. Lett. B (2009), 674(3):218-222.
[63]A. M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B (1981),103(3):207-210.
[64]V. Mukhanov, A. Wipf, and A. Zelnikov, On 4D Hawking radiation from the effective action, Phys. Lett. B (1994),332(3-4):283-291.
[65]V. P. Frolov, W. Israel, and S. N. Solodukhin, One-loop quantum corrections to the thermodynamics of charged black holes, Phys. Rev. D (1996),54(4):2732-2745.
[66]M. Buric, V. Radovanovic, and A. Mikovic, One-loop corrections for a Schwarzschild black hole via 2D dilaton gravity, Phys. Rev. D (1999),59(8):084002.
[67]F. C. Lombardo, F. D. Mazzitelli, and J. G. Russo, Energy-momentum tensor for scalar fields cou-pled to the dilaton in two dimensions, Phys. Rev. D (1999),59(6):064007.
[68]S. Nojiri and S. D. Odintsov, Trace-anomaly-induced effective action for 2D and 4D dilaton coupled scalars, Phys. Rev. D (1998),57(4):2363-2371.
[69]W. Kummer and D. V. Vassilevich, Hawking radiation from dilaton gravity in 1+1 dimensions:a pedagogical review, Ann. Phys. (Leipzig) (1999),8(10):801-827.
[70]R. Balbinot and A. Fabbri, Two-dimensional black holes and effective actions, Class. Quantum. Grav. (2003),20(24):5439-5454.
[71]R. Balbinot and A. Fabbri, Hawking radiation by effective two-dimensional theories, Phys. Rev. D (1999),59(4):044031.
[72]R. Balbinot and A. Fabbri,4D quantum black hole physics from 2D models? Phys. Lett. B (1999), 459(1-3):112-118.
[73]R. Balbinot, A. Fabbri, and I. Shapiro, Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions, Nucl. Phys. B (1999),559(1-2):301-319.
[74]S. Gangopadhyay, Hawking radiation from the Garfinkle-Horowitz-Strominger black hole, effective action, and covariant boundary condition, Phys. Rev. D (2008),77(6):064027.
[75]S. Kulkarni, Hawking fluxes, back reaction and covariant anomalies, Class. Quant. Grav. (2008), 25(22):225023.
[76]R. Banerjee and B.R. Majhi, Hawking black body spectrum from tunneling mechanism, Phys. Lett. B (2009),675(2):243-245.
[77]S. Q. Wu, General Nonextremal Rotating Charged Godel Black Holes in Minimal Five-Dimensional Gauged Supergravity, Phys. Rev. Lett. (2008),100(12):121301.
[78]R. C. Myers and M. J. Perry, Black holes in higher dimensional space-times, Ann. Phys. (N.Y.) (1986),172(2):304-347.
[79]S. Q. Wu, Separability of the massive Dirac equation in 5-dimensional Myers-Perry black hole geometry and its relation to a rank-three Killing-Yano tensor, Phys. Rev. D (2008),78(6):064052.
[80]J. Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity, Adv. Theor. Math. Phys. (1998),2(2):231-252.
[81]S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B (1998),428(1-2):105.
[82]E. Witten, Anti de Sitter Space and Holography, Adv. Theor. Math. Phys. (1998),2(2):253-290.
[83]O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. (2000),323(3-4):183-386.
[84]A. Strominger, Black hole entropy from near-horizon microstates, JHEP (1998),9802:009.