论文标题
无效边界的协变相空间
Covariant phase space with null boundaries
论文作者
论文摘要
通过强加与零边界的边界结构相关的边界条件，而不是通常的边界结构，我们发现在整个协变量相空间中，Harlow-Wu算法中的密钥要求无法满足。取而代之的是，它可以通过爱因斯坦重力中的无膨胀和无剪切曲面给出的无延伸性发出的空边界来满足，这可以被视为瓦尔德 - zoupas的处方方面的无处界限的起源。但是，尽管如此，通过遵守我们的指导原则，并将Harlow-Wu的算法适应上述的Submanifold，我们成功地繁殖了先前由Wald-Zoupas的处方获得的Hamiltonians，我们不仅在自然而然地定义了HAMINT，因此我们不仅可以自由地定义了Hamil，因此可以自由地定义了Hamil的定义。对于这种定义，也自然而然地登上了正确的边界项。
By imposing the boundary condition associated with the boundary structure of the null boundaries rather than the usual one, we find that the key requirement in Harlow-Wu's algorithm fails to be met in the whole covariant phase space. Instead, it can be satisfied in its submanifold with the null boundaries given by the expansion free and shear free hypersurfaces in Einstein's gravity, which can be regarded as the origin of the non-triviality of null boundaries in terms of Wald-Zoupas's prescription. But nevertheless, by sticking to the variational principle as our guiding principle and adapting Harlow-Wu's algorithm to the aforementioned submanifold, we successfully reproduce the Hamiltonians obtained previously by Wald-Zoupas' prescription, where not only are we endowed with the expansion free and shear free null boundary as the natural stand point for the definition of the Hamiltonian in the whole covariant phase space, but also led naturally to the correct boundary term for such a definition.
