论文标题
鹰辐射的半古典动力学
Semiclassical Dynamics of Hawking Radiation
论文作者
论文摘要
我们考虑在3+1个时空尺寸中的重力，并在半经典限制中以$ n \ to \ infty $耦合到$ n $标量质量字段。黑洞的动态演化包括公制上霍金辐射的后反应作为初始值问题。使用沿间距大地测量的点分裂正则化评估量子应力能量张量。为了说明物质磁场的量子纠缠，它们被视为在空超曲面上定义的一组双向集体场。由此产生的半经典字段方程包括衍生物中最多可容纳第四阶的术语，可以在扰动$ \ hbar $扩展中进行处理。我们得出的公式应该适合对时间依赖性半经典时空的数值模拟。
We consider gravity in 3+1 spacetime dimensions coupled to $N$ scalar matter fields in a semiclassical limit where $N\to\infty$. The dynamical evolution of a black hole including the back-reaction of the Hawking radiation on the metric is formulated as an initial value problem. The quantum stress energy tensor is evaluated using a point splitting regularization along spacelike geodesics. To account for the quantum entanglement of the matter fields, they are treated as a set of bilocal collective fields defined on spacelike hypersurfaces. The resulting semiclassical field equations include terms up to fourth order in derivatives that can be treated in a perturbative $\hbar$ expansion. The formulation we arrive at should be amenable to numerical simulation of time dependent semiclassical spacetime.
