Vacuum Black Hole Mass Formula Is a Vanishing Noether Charge |
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| Authors: | WU Xiao-ning GUO Han-ying HUANG Chao-Guang WU Ke |
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| Institution: | Institute of Theoretical Physics, the Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China Institute of Theoretical Physics, the Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China Institute of High Energy Physics, the Chinese Academy of Sciences, P.O. Box 9184, Beijing 100039, China;Institute of Theoretical Physics, the Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China Institute of Theoretical Physics, the Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China;Departrnent of Mathematics, Capital Normal University, Beijing 100037, China |
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| Abstract: | The Noether current and its variation relation with respect to diffeomorphism invariance of gravitationaltheories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respec-tively. For Einstein's GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived fromthis Noether current although it definitely vanishes. This indicates that the mass formula of black holes is a vanishingNoether charge in this case. The first law of black hole thermodynamics can also be derived from the variation relationof this vanishing Noether current. |
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| Keywords: | black hole mass formula Noether charge diffeomorphism invariance |
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