We scrutinize the conserved energy of an accelerating AdS black hole by employing the off-shell quasilocal formalism, which amalgamates the ADT formalism with the covariant phase space approach. In the presence of conical singularities in the accelerating black hole, the energy expression is articulated through the surface term derived from our formalism. The essence of our analysis of the quasilocal energy resides in the surface contributions coming from the conical singularities as well as the conventional radial boundary. Consequently, the resultant conserved quasilocal energy naturally conforms the thermodynamic first law for the black hole without necessitating any augmentation of thermodynamic variables.

中文翻译：

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加速AdS黑洞的准局域能量和热力学第一定律


我们通过采用离壳准局域形式主义（将 ADT 形式主义与协变相空间方法合并）来仔细研究加速 AdS 黑洞的守恒能量。在加速黑洞中存在圆锥形奇点的情况下，能量表达式是通过源自我们形式主义的表面项来表达的。我们对准局域能量分析的本质在于来自圆锥奇点以及传统径向边界的表面贡献。因此，由此产生的守恒准局域能量自然符合黑洞的热力学第一定律，而无需增加任何热力学变量。