论文标题
通过热内核静态间距中的非本地标量场
Non-local scalar fields in static spacetimes via heat kernels
论文作者
论文摘要
我们解决了静态spaceTimes中的静态标量字段和ii）超级示波器中的时间依赖性标量字段。相应的方程被用静态/频域绿色的函数重写为紧凑和非紧凑的加权/riemannian歧管中的非本地泊松/不均匀的Helmholtz方程，可以从相应流式中的热中计算出来。借助热核估计值，我们得出了静态绿色的功能估计，并使用它们来讨论规律性。我们还提供了几个示例，示例是精确和估计的静态/频域绿色功能。
We solve the non-local equation ${-e^{-\ell^2\square}\squareϕ=J}$ for i) static scalar fields in static spacetimes and ii) time-dependent scalar fields in ultrastatic spacetimes. Corresponding equations are rewritten as non-local Poisson/inhomogeneous Helmholtz equations in compact and non-compact weighted/Riemannian manifolds using static/frequency-domain Green's functions, which can be computed from the heat kernels in the respective manifolds. With the help of the heat kernel estimates, we derive the static Green's function estimates and use them to discuss the regularity. We also present several examples of exact and estimated static/frequency-domain Green's functions.
