论文标题
关于真空爱因斯坦方程和几何唯一性的初始边界价值问题
On the initial boundary value problem for the vacuum Einstein equations and geometric uniqueness
论文作者
论文摘要
我们通过描述其相关仪表中的时空度量的边界条件来为真空爱因斯坦方程提出初始边界值问题（IBVP）。该规格是通过时空度量标准地确定的，相对于差异性。真空时空度量$ g $及其相关的量规$ ϕ_g $在本地谐波坐标中同时解决。此外，我们表明，满足固定的初始条件和拐角条件的真空空间在初始表面附近是几何独特的。最后，类似于凯奇问题的解决方案，我们还构建了IBVP的独特全球双曲线解。
We formulate an initial boundary value problem (IBVP) for the vacuum Einstein equations by describing the boundary conditions of a spacetime metric in its associated gauge. This gauge is determined, equivariantly with respect to diffeomorphisms, by the spacetime metric. The vacuum spacetime metric $g$ and its associated gauge $ϕ_g$ are solved simultaneously in local harmonic coordinates. Further we show that vacuum spacetimes satisfying fixed initial-boundary conditions and corner conditions are geometrically unique near the initial surface. Finally, in analogy to the solution of the Cauchy problem, we also construct a unique maximal globally hyperbolic solution of the IBVP.
