The purpose of this paper is to enhance the conventional Komar integral to asymptotically anti-de Sitter (AdS) black holes. In order to do so, we first obtain a potential that is the linear combination of the usual Komar potential with two third-order derivative terms generated by the action of the d’Alembertian operator and the exterior derivative upon a Killing vector. Then this higher-order corrected potential is extended to the Einstein gravity with a negative cosmological constant, yielding the potential that is the linear combination of the usual Komar one with it acted on by the d’Alembertian. It is demonstrated that the surface integral of the improved Komar potential can serve as a formula for conserved charges of asymptotically AdS spacetimes. Finally, to illustrate such a formula, we make use of it to compute the mass and the angular momentum of Schwarzschild-AdS black holes, regular AdS black holes, asymptotically AdS Kerr-Sen black holes, Kerr-NUT-AdS black holes, and Kerr-AdS black holes in arbitrary dimensions. The results are in agreement with the ones in the literature.

本文的目的是将传统的 Komar 积分增强为渐近反德西特 (AdS) 黑洞。为了做到这一点，我们首先获得一个势，它是通常的 Komar 势与两个三阶导数项的线性组合，这些项是由 d'Alembertian 算子和Killing 向量的外部导数的作用产生的。然后这个高阶修正势被扩展到爱因斯坦引力，宇宙常数为负，产生的势是通常的 Komar 势与它由 d'Alembertian 作用的线性组合。证明了改进的 Komar 势的表面积分可以作为渐近 AdS 时空的守恒电荷的公式。最后，为了说明这样一个公式，我们利用它来计算任意维度的 Schwarzschild-AdS 黑洞、规则 AdS 黑洞、渐近 AdS Kerr-Sen 黑洞、Kerr-NUT-AdS 黑洞和 Kerr-AdS 黑洞的质量和角动量. 结果与文献中的结果一致。