标题： 静态球对称时空中标量场量子化的应力-能量张量的解析近似 显示英文标题

标题： Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes

摘要： 得到了静态球对称时空中标量场量子化的${< \phi^2 >}$和${< T^{\mu}_{\nu} >}$的解析近似。 假设该场既具有质量又无质量，并且与标量曲率有任意耦合$\xi$，在零温度的真空态下。 ${< \phi^2 >}$和${< T^{\mu}_{\nu} >}$的表达式被分为低频和高频两部分。 对于任意量子态，计算了高频模对这些量的贡献。 作为一个例子，在渐近平直时空中，计算了对应于闵可夫斯基真空（Boulware 量子态）的量子态下，${< \phi^2 >}$和${< T^{\mu}_{\nu} >}$的低频贡献。 讨论了这些近似的适用范围。 显示英文摘要

摘要： Analytical approximations for ${< \phi^2 >}$ and ${< T^{\mu}_{\nu} >}$ of a quantized scalar field in static spherically symmetric spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state. The expressions for ${< \phi^2 >}$ and ${< T^{\mu}_{\nu} >}$ are divided into low- and high-frequency parts. The contributions of the high-frequency modes to these quantities are calculated for an arbitrary quantum state. As an example, the low-frequency contributions to ${< \phi^2 >}$ and ${< T^{\mu}_{\nu} >}$ are calculated in asymptotically flat spacetimes in a quantum state corresponding to the Minkowski vacuum (Boulware quantum state). The limits of the applicability of these approximations are discussed.