论文标题
静态间距中的半经典重力作为约束的初始值问题
Semiclassical gravity in static spacetimes as a constrained initial value problem
论文作者
论文摘要
我们在超级和静态空间中使用klein-gordon场研究了半经典的爱因斯坦田间方程。在这两种情况下，时空度量的方程式成为约束方程。在超级情况下，可以明确表征Hadamard的奇异结构，这原理可以为Wightman函数提供具有正确分布奇异性的Wightman函数的初始数据，因此可以定义恢复型应力的应激能量张量的期望值，从而可以被定义，从而使半经典的EINSTEINEETICATION可以理解。假设Klein-Gordon操作员有“正能量”条件，我们表征了这些状态，如果限制存在于初始数据，则它们在时空中无处不在。这些事实证明是时间翻译的状态。通过共形技术对静态病例进行了分析，从而有效地将问题降低到了超级问题。
We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard singular structure can be characterised explicitly, which allows one to in principle give initial data for the Wightman function that has correct distributional singularities, such that the expectation value of the renormalised stress-energy tensor of the solution can be defined, and that hence the semiclassical Einstein equations make sense. Assuming a "positive energy" condition for the Klein-Gordon operator, we characterise the states for which, if the constraints hold for initial data, they hold everywhere in spacetime. These turn out to be time-translation invariant states. The static case is analysed by conformal techniques, effectively reducing the problem to an ultrastatic one.
