Noether Theorem and Black Hole's Mass Formula and Entropy

HUANG Chao-Guang; GUO Han-Ying; WU Xiao-Ning

Chinese Physics C> 2003, Vol. 27> Issue(10) : 879-883

Noether Theorem and Black Hole's Mass Formula and Entropy

Institute of High Energy Physics,CAS,Beijing 100039,China2 Institute of Theoretical Physics,CAS,Beijing 100080,China3 Max-Plank-Insitut filr Gravitationsphysik,14476,Golm,Germany

Abstract
HTML
Reference
Related

PDF

Abstract：
The Noether charge formalism on the covariant phase space is used and developed. For a stationary axisym-metric black hole in vacuum general relativity, the mass formula is the vanishing Noether charge with respect to the Killing vector field an entire Cauchy surface. Its differential form gives the first law of black hole mechanics . For a large class of vector fields, the central term of the reduced algebra near the horizon is proved to be zero by use of the null tetrad formalism. It implies that the microscopic interpretation of the black hole entropy based on the symmetry analysis proposed by Carlip is debatable.

References

[1]

Wald R M. Phys. Rev., 1993, D48: R3427; Living Rev. Rel., 2001, 4(6) : 12 Carlip S. Class. Quan. Gray., 1999, 16:3327; Nucl. Phys. Proc. Suppl., 2000, 88:10; Phys. Rev. Lett., 2002, 88:241301 3 Cardy J A. Nucl. Phys. 1986, B270:1864 WU Xiao–Ning, GUO Han–Ying, HUANG Chao–Guang et al. Commun. Theor. Phys. , 2002, 38 : 309 5 GUO Han–Ying, HUANG Chao–Guang, WU Xiaoning. Phys. Rev. 2003, D67 : 024031 6 Bardeen J M et al. Commun. Math. Phys., 1973, 31:161

[1]	XU Chang , REN Zhong-Zhou , WANG Zai-Jun . New Formula for Spontaneous Fission Half-lives of Heavy Nuclei. Chinese Physics C, 2005, 29(7): 673-676.
[2]	LU Dao-Ming . Evolution of Field Entropy in the Multiphoton Jaynes-Gummings Model. Chinese Physics C, 2005, 29(4): 435-438.
[3]	BAI Hua , YAN Mo-Lin . Generalize 't Hooft's Quantum State of the Black Hole Theory. Chinese Physics C, 2005, 29(12): 1136-1141.
[4]	ZUO Wei , LI Zeng-Hua , LIU Jian-Ye , LI Jun-Qing . Properties of Isospin Asymmetric Nuclear Matter and Extended BHF Approach (Ⅲ) HVH Theorem and Fermi Energy. Chinese Physics C, 2003, 27(1): 31-35.
[5]	LI Zi-Ping . Noether Identities at the Quantum Level. Chinese Physics C, 2002, 26(3): 230-238.
[6]	Pan Zhongcheng , Jiang Shaozhou , Gao Liangjun . Probability Distribution and Entropy of Nonequilibrium State for ²⁰⁸Pb Nuclei Under Different Excited Energies. Chinese Physics C, 1995, 19(8): 757-763.
[7]	Li Ziping . Generalization and Application of the Noether's Identities. Chinese Physics C, 1995, 19(S2): 157-163.
[8]	Zhong Yunxiao , Hu Jimin . Study of the Multidimensional Kramers'Equation. Chinese Physics C, 1994, 18(10): 949-954.
[9]	XU Fuxin , XU Ni . A Comprehensive Analysis for Eight Formulas for Rotational Spectra. Chinese Physics C, 1993, 17(11): 1040-1047.
[10]	PAN Zhong-Cheng , JIANG Shao-Zhou , GAO Liang-Jun , LONG Sheng-Dong . Instantaneous Probability Distribution and Nonequilibrium Entropy of Nuclear Exciton States. Chinese Physics C, 1993, 17(5): 444-447.
[11]	LIU Jian-Ye , YANG Fu-Zhong . Entropy Production,Collision Number and the Forming Process of Hot Nucleus. Chinese Physics C, 1992, 16(5): 468-474.
[12]	GAN Zai-Guo , HUANG Ye-Cheng . A Mass Formula with a Few Free Parameters and Nuclear Mass Calculations. Chinese Physics C, 1992, 16(2): 172-177.
[13]	WU Yuan-Fang , LIU Lian-Shou . Conditional Entropy and Mutual Information in Random Cascading Processes. Chinese Physics C, 1991, 15(8): 711-714.
[14]	MENG Jie , YIN Chuan-Zong , LIN Xin-Wei . A Simple Formula for Backbending. Chinese Physics C, 1991, 15(12): 1109-1114.
[15]	HUANG Hai-Xin , LIN Xin-Wei , ZENG Jin-Yan . COMPARISON BETWEEN HARRIS AND WU-ZENG'S FORMULAS FOR ROTATIONAL SPECTRA OF DEFORMED NUCLEI. Chinese Physics C, 1989, 13(8): 744-751.
[16]	LI Zi-Ping . THE GENERALIZED NOETHER'S IDENTITIES AND CONSERVED CHARGE. Chinese Physics C, 1988, 12(6): 782-785.
[17]	QUAN Xiang-Lin , WANG Lian-Ji . THE GENERALIZATION ON B.W.LEE'S EQUATION Γ*Γ=0. Chinese Physics C, 1986, 10(4): 508-512.
[18]	ZENG JIN-YAN , LIN CHUN-ZHENG , YANG FU-JIA . A CHECK ON INDIVIDUAL TERMS OF THE NUCLEAR MASS FORMULA. Chinese Physics C, 1981, 5(2): 232-243.
[19]	Bao Cheng-guang . THE OPTICAL THEOREM AND A COMPLETE SET OF A MANY BODY SYSTEM LABELLED BY DIFFERENT CHANNEL STATES. Chinese Physics C, 1980, 4(5): 623-625.
[20]	CHEN JIN-QUAN , YU ZU-RONG , WANG FAN . A RECURSIVE FORMULA FOR THE CLEBSCH-GORDAN COEFFICIENTS OF SU_n GROUP. Chinese Physics C, 1979, 3(2): 216-255.

Access

Get Citation

HUANG Chao-Guang, GUO Han-Ying and WU Xiao-Ning. Noether Theorem and Black Hole's Mass Formula and Entropy[J]. Chinese Physics C, 2003, 27(10): 879-883.

HUANG Chao-Guang, GUO Han-Ying and WU Xiao-Ning. Noether Theorem and Black Hole's Mass Formula and Entropy[J]. Chinese Physics C, 2003, 27(10): 879-883. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2003-03-19
Revised: 1900-01-01

Article Metric

Article Views(4331)
PDF Downloads(586)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Noether Theorem and Black Hole's Mass Formula and Entropy

Corresponding author: HUANG Chao-Guang,

Institute of High Energy Physics,CAS,Beijing 100039,China2 Institute of Theoretical Physics,CAS,Beijing 100080,China3 Max-Plank-Insitut filr Gravitationsphysik,14476,Golm,Germany

Received Date: 2003-03-19
Accepted Date: 1900-01-01
Available Online: 2003-10-05

Abstract: The Noether charge formalism on the covariant phase space is used and developed. For a stationary axisym-metric black hole in vacuum general relativity, the mass formula is the vanishing Noether charge with respect to the Killing vector field an entire Cauchy surface. Its differential form gives the first law of black hole mechanics . For a large class of vector fields, the central term of the reduced algebra near the horizon is proved to be zero by use of the null tetrad formalism. It implies that the microscopic interpretation of the black hole entropy based on the symmetry analysis proposed by Carlip is debatable.