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

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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

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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

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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

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

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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.