弯曲时空上的无切变射线同余
Shear-free ray congruences on curved space-times
摘要：
闵可夫斯基空间上的无切变射线同余是一个3参数零测地线族，沿着它，互补的2维类空子空间（称为屏空间）的李输运是共形的。这种同余由相应扭量空间$\CP^3$中的复解析曲面定义，是构造无质量场的基础。在更一般的时空中，如何将无质量场与引力场耦合起来还不清楚。在本文中，我们通过考虑以下柯西型问题来做到这一点：给定一个黎曼3-流形$(M^3, g_0)$，该流形具有一个与共形叶理相切的单位向量场$U_0$，我们要求这个对延伸到一个空间-时间$({\mathcal M}, {\mathcal G})$被赋予类空单位向量场$U_t$，使得$U_t$同时产生零测地线并与类空切片上的共形叶理相切$t=$常量
英文摘要：
A shear-free ray congruence on Minkowski space is a 3-parameter family of null geodesics along which Lie transport of a complementary 2-dimensional spacelike subspace (called the screen space) is conformal. Such congruences are defined by complex analytic surfaces in the associated twistor space $\CP^3$ and are the basis of the construction of massless fields. On a more general space-time, it is unclear how to couple the massless field with the gravitational field. In this article we do this by considering the following Cauchy-type problem: given a Riemannian 3-manifold $(M^3, g_0)$ endowed with a unit vector field $U_0$ that is tangent to a conformal foliation, we require that the pair extend to a space-time $({\mathcal M}, {\mathcal G})$ endowed with a spacelike unit vector field $U_t$ in such a way that $U_t$ simultaneously generates null geodesics and is tangent to a conformal foliation on spacelike slices $t=$ const.
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