中科院数学与系统科学研究院
数学研究所
学术报告
数学物理研讨班
报告人：高思杰 教授 （北京师范大学）
题 目：General mass formulas for charged Kerr-AdS black holes
时 间：2023.08.11（星期五）19:00-20:00
地 点：腾讯会议 714 148 202
摘 要：It is well-known that the mass of a non-asymptotically flat spacetime cannot be uniquely defined. A reasonable definition of mass for the Kerr-AdS black hole has been found and widely used in studying black hole thermodynamics. However, the derivation usually needs a background subtraction to eliminate the divergence. It is also unknown whether this formula can be extended to a more general form. In this paper, we provide a more straightforward derivation for the mass formula, only demanding that the first law of black hole thermodynamics and Smarr formula are satisfied. We first make use of the Iyer-Wald formalism to derive a first law of charged Kerr-AdS black hole in the extended phase space. However, this mass is obviously not integrable. We then modify the coefficients of the first law to make the mass integrable. Finally, by applying the scaling argument to the modified first law, we obtain the Smarr formula, i.e., the explicit form of the mass. Remarkably, our mass formula contains a free parameter and when it is set to zero, we recover the familiar mass formula in the literature. Moreover, by making use of the gauge freedom of the Killing vector field, we find a favorite parameter t’ which just gives the first law and makes the mass integrable. This mass formula has not been widely noticed, and could have important applications in future studies.
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