Noether定理与黑洞的质量公式及黑洞熵

Noether Theorem and Black Hole's Mass Formula and Entropy

运用并发展了协变相空间的Noether荷方法,对于真空广义相对论稳态轴对称黑洞得到:黑洞质量公式是关于Killing向量场和完整Cauchy面上的零Noether荷以及黑洞力学第一定律。对于一大类向量场,利用零标架方法证明在视界附近的约化代数的中心项为零。这表明,Carlip用纯粹对称性分析的方法来解释黑洞熵的微观起源值得商榷。

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.