标题： 高阶导数对NNLO下黑洞热力学的贡献 显示英文标题

标题： Higher derivative contributions to black hole thermodynamics at NNLO

摘要： 在引力的有效理论中，黑洞的热力学量会受到高阶导数项无限级数的修正。 在下一级近似中，这些量仅通过领先阶解即可获得。 在本文中，我们将这一特性推进到下下一级近似。 我们提出一个公式，仅使用到下一级近似解即可得到渐近平坦黑洞在下下一级近似下的欧几里得作用量。 其他守恒量则通过标准热力学关系从欧几里得作用量中推导得出。 我们在$D$维纯引力和包含四阶和六阶导数项的爱因斯坦-麦克斯韦理论的例子中验证了我们的公式。 基于我们的公式，我们还证明了对于渐近平坦黑洞，物理量在场重定义下是不变的。 显示英文摘要

摘要： In an effective theory of gravity, thermodynamic quantities of black holes receive corrections from the infinite series of higher derivative terms. At the next to leading order, these can be obtained by using only the leading order solution. In this paper, we push forward this property to the next to next to leading order. We propose a formula which yields the Euclidean action of asymptotically flat black holes at the next to next to leading order using only the solution up to and including the next to leading order. Other conserved quantities are derived from the Euclidean action via standard thermodynamic relation. We verify our formula in examples of $D$-dimensional pure gravity and Einstein-Maxwell theory extended by 4- and 6-derivative terms. Based on our formula, we also prove that for asymptotically flat black holes, the physical quantities are invariant under field redefinitions.