标题： 渐近Lifshitz黑洞中的真空极化 显示英文标题

标题： Vacuum polarization in asymptotically Lifshitz black holes

摘要： 对将规范/引力对偶应用于具有特定关注的凝聚态理论的兴趣很大，特别关注于表现出各向异性缩放的理论的引力对偶（Lifshitz时空）。在此背景下，也构建了具有Lifshitz渐近的黑洞解，旨在包含有限温度效应。这里的目标是研究这些时空中的量子极化效应，并为此，我们开发了一种计算质量性非最小耦合标量场的格林函数的重合极限的方法，将为渐近反德西特黑洞情况开发的分析适应到当前情况。基本方法与之前的计算类似，然而在Lifshitz情况下需要扩展之前的结果以包括度规的更一般形式和对动态指数的依赖。一旦将动态指数的值设为1，并相应地选择度规函数，所有公式都被证明会还原到之前研究的AdS情况。我们提出的解析结果是通用的，可以应用于各种情况，事实上，适用于所有球对称的Lifshitz黑洞解。我们还进行了数值分析，选择了一些已知的Lifshitz黑洞解作为例子。 显示英文摘要

摘要： There has been considerable interest in applying the gauge/gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed aiming at incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes, and to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, non-minimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti de Sitter black holes. The basics are similar to previous calculations, however in the Lifshitz case one needs to extend previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulae are shown to reduce to the AdS case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.