标题： 通过广义zeta函数方法研究AdS空间中应力-能量张量的相关性 显示英文标题

标题： Correlations of the stress-energy tensor in AdS spaces via the generalized zeta-function method

摘要： 我们计算了在反德西特（AdS）空间中，一个最小耦合的无质量标量场的应力-能量双张量的真空期望值。 这些关联函数也被称为噪声核，在随机引力的爱因斯坦-朗之万方程[1,2]中作为源项，这些方程描述了由半经典引力的半经典爱因斯坦方程所描述的平均场动力学之外的诱导度规涨落。 由于AdS空间是最大对称的，本征模式具有解析表达式，这有助于zeta函数的计算[3,4]。 通过对[5]中引入的广义zeta函数进行第二次泛函变分，我们得到了应力张量的关联函数。 给出了关联函数的短和长测地线距离极限。 显示英文摘要

摘要： We calculate the vacuum expectation values of the stress-energy bitensor of a minimally coupled massless scalar field in anti-de Sitter (AdS) spaces. These correlators, also known as the noise kernel, act as sources in the Einstein-Langevin equations of stochastic gravity [1,2] which govern the induced metric fluctuations beyond the mean-field dynamics described by the semiclassical Einstein equations of semiclassical gravity. Because the AdS spaces are maximally symmetric the eigenmodes have analytic expressions which facilitate the computation of the zeta-function [3,4]. Upon taking the second functional variation of the generalized zeta function introduced in [5] we obtain the correlators of the stress tensor. Both the short and the long geodesic distance limits of the correlators are presented.