Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Front. Phys.    2009, Vol. 4 Issue (4) : 530-533    https://doi.org/10.1007/s11467-009-0070-2
Research articles
Fluctuation around horizon on a Schwarzschild black hole using the null geodesic method
Ji-li HUANG(黄基利),Wen-biao LIU(刘文彪),
Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing 100875, China;
 Download: PDF(169 KB)  
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract Using the null geodesic method, Hawking radiation from the horizon of a Schwarzschild black hole is calculated. The thermodynamics can be built successfully on the horizon where the apparent horizon and event horizon are coincident with each other. When a relativistic perturbation is given to the horizon, the first law of thermodynamics can also be constructed at a new supersurface near the horizon successfully. The expressions of the characteristic position and temperature are consistent with the previous result while the thermodynamics was built on the event horizon in a Vaidya black hole. Therefore, the thermodynamics of a dynamical black hole should be constructed on the apparent horizon exactly, and the event horizon thermodynamics is just one of the perturbations near the apparent horizon.
Keywords Hawking radiation      thermodynamics      dynamical black hole      apparent horizon      event horizon      
Issue Date: 05 December 2009
 Cite this article:   
Ji-li HUANG(黄基利),Wen-biao LIU(刘文彪). Fluctuation around horizon on a Schwarzschild black hole using the null geodesic method[J]. Front. Phys. , 2009, 4(4): 530-533.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-009-0070-2
https://academic.hep.com.cn/fop/EN/Y2009/V4/I4/530
S. W. Hawking, Commun. Math. Phys., 1975, 43(3): 199

doi: 10.1007/BF02345020
J. B. Hartle and S. W. Hawking, Phys. Rev. D, 1975, 13: 2188

doi: 10.1103/PhysRevD.13.2188
M. K. Parikh and F. Wilczek, Phys. Rev. Lett., 2000, 85: 5042

doi: 10.1103/PhysRevLett.85.5042
K. Srinivasam and T. Padmanabhan, Phys. Rev. D, 1999, 60: 024001

doi: 10.1103/PhysRevD.60.024001
W. B. Liu, Acta Physica. Sinica, 2007, 56(10): 6164
Q. Q. Jiang, S. Q. Wu, and X. Cai, Phys. Rev. D, 2006, 73: 064003

doi: 10.1103/PhysRevD.73.064003
Y. P. Hu, J. Y. Zhang, and Z. Zhao, Mod. Phys. Lett. A, 2006, 21: 2143

doi: 10.1142/S0217732306020184
Z. B. Xu and B. Chen, Phys. Rev. D, 2007, 75: 024041

doi: 10.1103/PhysRevD.75.024041
R. Kerner and R. B. Mann, Class. Quantum Grav., 2008, 25: 195014

doi: 10.1088/0264-9381/25/9/095014
R. D. Criscienzo and L. Vanzo, Europhys. Lett., 2008, 82: 60001

doi: 10.1209/0295-5075/82/60001
D. Y. Chen, Q. Q. Jiang, S. Z. Yang, and X. T. Zu, Class. Quantum Grav., 2008, 25: 205022

doi: 10.1088/0264-9381/25/20/205022
J. M. Bardeen and S. W. Hawking, Commun. Math. Phys., 1973, 31: 161

doi: 10.1007/BF01645742
J. D. Beekenstein, Phys. Rev. D, 1973, 7: 2233
R. M. Wald, Phys. Rev. D, 1979, 20: 1271

doi: 10.1103/PhysRevD.20.1271
R. Balbinot, Phys. Rev. D, 1986, 33: 1611

doi: 10.1103/PhysRevD.33.1611
J. Ren, J. Y. Zhang, and Z. Zhao, Chin. Phys. Lett., 2006, 23: 2019

doi: 10.1088/0256-307X/23/8/016
E. C. Vagenas and S. Das, JHEP, 2006, 0610: 025
G. Fodor, K. Nakamura, Y. Oshiro, and A. Tomimatsu, Phys. Rev. D, 1996, 54: 3882

doi: 10.1103/PhysRevD.54.3882
P. Hajicek, Phys. Rev. D, 1987, 36: 1065

doi: 10.1103/PhysRevD.36.1065
W. A. Hiscock, Phys. Rev. D, 1989, 40: 1336

doi: 10.1103/PhysRevD.40.1336
W. Collins, Phys. Rev. D, 1992, 45: 495

doi: 10.1103/PhysRevD.45.495
S. A. Hayward, Phys. Rev. D, 1994, 49: 6467

doi: 10.1103/PhysRevD.49.6467
S. A. Hayward, Phys. Rev. Lett., 2004, 93: 251101

doi: 10.1103/PhysRevLett.93.251101
S. A. Hayward, Phys. Rev. D, 2004, 70: 104027

doi: 10.1103/PhysRevD.70.104027
A. Ashtekar and B. Krishman, Phys. Rev. D, 2003, 68: 104030

doi: 10.1103/PhysRevD.68.104030
A. B. Nielsen, arXiv:hep-th/0809.3850, 2008
E. Gourgoulhon and J. L. Jaramillo, New Astronomy Reviews, 2008, 51: 791

doi: 10.1016/j.newar.2008.03.026
X. M. Liu and W. B. Liu, Where does Hawkingradiation of a dynamical black hole come from? (to be published)
T. Zhu, J. R. Ren, and D. Singleton, arXiv: hepth/0902.2542v1, 2009
[1] Zhan-Chun Tu. Abstract models for heat engines[J]. Front. Phys. , 2021, 16(3): 33202-.
[2] Zhen-Ming Xu (许震明). Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space[J]. Front. Phys. , 2021, 16(2): 24502-.
[3] Hui-Juan Xu, Tong Tong, Rui-Zheng Hou, Hong-Rong Li. Reconceptualizing kinesin’s working cycle as separate chemical and mechanical processes[J]. Front. Phys. , 2018, 13(5): 138206-.
[4] Ting-Hua Li (李廷华),Dong-Lai Zhu(朱东来),Fu-Chun Mao(毛福春),Ming Huang(黄铭),Jing-Jing Yang(杨晶晶),Shou-Bo Li. Design of diamond-shaped transient thermal cloaks with homogeneous isotropic materials[J]. Front. Phys. , 2016, 11(5): 110503-.
[5] Mahamat Saleh,Bouetou Thomas Bouetou,Timoleon Crepin Kofane. Hawking radiation from a five-dimensional Lovelock black hole[J]. Front. Phys. , 2015, 10(5): 100401-.
[6] Li-fang SONG (宋莉芳), Chun-hong JIANG (姜春红), Shu-sheng LIU (刘淑生), Cheng-li JIAO (焦成丽), Xiao-liang SI (司晓亮), Shuang WANG (王爽), Fen LI (李芬), Jian ZHANG (张箭), Li-xian SUN (孙立贤), Fen XU (徐芬), Feng-lei HUANG (黄风雷). Progress in improving thermodynamics and kinetics of new hydrogen storage materials[J]. Front. Phys. , 2011, 6(2): 151-161.
[7] Han DING (丁翰), Wen-biao LIU (刘文彪). Hawking radiation from a Vaidya black hole by Hamilton–Jacobi method[J]. Front. Phys. , 2011, 6(1): 106-108.
[8] Bo LIU (刘博), Wen-biao LIU(刘文彪). The thermodynamics in a dynamical black hole[J]. Front Phys Chin, 2009, 4(1): 94-96.
[9] LANG Xing-you, JIANG Qing. Size dependence of phase transition temperatures of ferromagnetic, ferroelectric and superconductive nanocrystals[J]. Front. Phys. , 2007, 2(3): 289-311.
[10] WU Zhi-min, WU Zhi-min, WANG Xin-qiang, WANG Xin-qiang, XIAO Xu-yang, XIAO Xu-yang, HE Huan-dian, HE Huan-dian, LUO Qiang, LUO Qiang. Thermodynamic properties of noble metal clusters: molecular dynamics simulation[J]. Front. Phys. , 2006, 1(3): 351-356.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed