The initial boundary value problem in General Relativity: the umbilic case
The initial boundary value problem in General Relativity: the umbilic case
复制标题
广义相对论中的初始边值问题：脐带情况
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Jacques Smulevici
中科院分区：
文献类型：
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作者：
G. Fournodavlos;Jacques Smulevici
本文给出了广义相对论中具有唯一边界条件的初边值问题的局部适定性的一个简短证明。这包括作为特殊情况的完全测地边界条件，我们以前在[8]中处理过。证明是基于波坐标和关键的观察，动量约束总是有效的脐边界。这允许在边界条件的选择中有更大的自由度，因为施加脐条件也为四个波坐标条件中的三个提供了诺依曼边界条件。此外，脐条件是几何的，意味着弗里德里希意义上的几何唯一性在这个特定情况下成立。
We give a short proof of local well-posedness for the initial boundary value problem in general relativity with sole boundary condition the requirement that the boundary is umbilic. This includes as a special case the totally geodesic boundary condition that we had previously addressed in [8]. The proof is based on wave coordinates and the key observation that the momentum constraint is always valid for umbilic boundaries. This allows for a greater freedom in the choice of boundary conditions, since imposing the umbilic condition also provides Neumann boundary conditions for three of the four wave coordinates conditions. Moreover, the umbilic condition, being geometric, implies that geometric uniqueness in the sense of Friedrich holds in this specific case.
影响因子：
1.3
作者：
Carla Cederbaum;G. Galloway
通讯作者：
Carla Cederbaum;G. Galloway