论文标题
洛伦兹散射僵化问题和固定指标的刚度
The Lorentzian scattering rigidity problem and rigidity of stationary metrics
论文作者
论文摘要
我们研究洛伦兹几何形状中的散射刚度：从散射关系$ \ MATHCAL {S}^\ Sharp $中恢复了Lorentzian度量标准。我们表明，在非偶性假设下，每个定义函数$ r（x，y）的边界点$ $可以通过浅色的测量线连接起来，从以下意义上讲，边界距离函数在Riemannian情况下扮演着角色。它的线性化是二级量的张量场的灯光变换，这是度量标准的扰动。接下来，我们研究时间空间圆柱体中固定指标的散射刚度，并表明它可以将其简化为基座上磁系统的边界刚度。以前研究了一个问题。这意味着固定指标的几个散射刚度结果。
We study scattering rigidity in Lorentzian geometry: recovery of a Lorentzian metric from the scattering relation $\mathcal{S}^\sharp$ known on a lateral boundary. We show that, under a non-conjugacy assumption, every defining function $r(x,y)$ of pairs of boundary points which can be connected by a lightlike geodesic plays the role of the boundary distance function in the Riemannian case in the following sense. Its linearization is the light ray transform of tensor fields of order two which are the perturbations of the metric. Next, we study scattering rigidity of stationary metrics in time-space cylinders and show that it can be reduced to boundary rigidity of magnetic systems on the base; a problem studied previously. This implies several scattering rigidity results for stationary metrics.
