标题： 双-null叶状结构中的线性双曲方程 显示英文标题

标题： Linear hyperbolic equations in a double null foliation

摘要： 对于时空$(M, g)$中满足真空爱因斯坦方程的 Weyl 曲率张量，在双特征foliation下的 Bianchi 恒等式具有双曲结构，这一结构可用于获得关于零模式 Weyl 张量分量的详细非线性估计。 本文的目的有两个方面。 首先我们讨论任意时空下双特征foliation中一阶线性双曲方程组解的存在性和唯一性问题，初始数据设定在过去的一个零特征超曲面$\underline C_0 \cup C_0$上。 我们证明了这些系统全局存在且唯一的定理。 然后我们讨论这些系统、Bianchi 方程和线性化Bianchi方程之间的关系（通过用未知张量场替换零模式Weyl张量分量，从通常的Bianchi方程得到线性化Bianchi方程）。 我们推导出一个新颖的代数约束，该约束必须由满足线性化Bianchi方程的张量场在时空中的每一点处满足。 显示英文摘要

摘要： The Bianchi identities for the Weyl curvature tensor of a spacetime $(M, g)$ solving the vacuum Einstein equations in a double null foliation exhibit a hyperbolic structure, which can be used to obtain detailed nonlinear estimates on the null Weyl tensor components. The aim of this paper is twofold. First we discuss existence and uniqueness for solutions of first-order linear hyperbolic systems of equations in a double null foliation on an arbitrary spacetime, with initial data posed on a past null hypersurface $\underline C_0 \cup C_0$. We prove a global existence and uniqueness theorem for these systems. Then we discuss the relationship between these systems, the Bianchi equations, and the linearized Bianchi equations (the linearized Bianchi equations are obtained from the usual Bianchi equations by replacing the null Weyl tensor components with unknown tensorfields). We derive a novel algebraic constraint which must be satisfied, at every point in the spacetime, by tensorfields satisfying the linearized Bianchi equations.