论文标题
在边界差异空间上，绝热溶液作为无效的大地测量学
Adiabatic Solutions in General Relativity as Null Geodesics on the Space of Boundary Diffeomorphisms
论文作者
论文摘要
我们在绝热模式中使用类似于温伯格的技巧，在曼顿近似中，以实现空间边界的歧管的一般相对论。这导致将缓慢的依赖性解决方案描述为边界差异空间上的无效测量学，就度量而言，我们被证明仅由边界数据组成。我们展示了如何通过一般相对性的限制来确定批量空间中的解决方案。 为了使我们的描述具有更大的观点，我们此外，我们确定了我们所产生的拉格朗日人作为Continuum Mechanics的协变量Lagrangian的广义版本。我们研究了3+1和2+1维的病例，并显示了我们提出的解决方案，在两个空间维度的特殊情况下，哈密顿的约束成为真正的同质蒙格 - 安培方程。
We use a trick similar to Weinberg's for adiabatic modes, in a Manton approximation for general relativity on manifolds with spatial boundary. This results in a description of the slow-time dependent solutions as null geodesics on the space of boundary diffeomorphisms, with respect to a metric we prove to be composed solely of the boundary data. We show how the solutions in the bulk space is determined with the constraints of general relativity. To give our description a larger perspective, we furthermore identify our resulting Lagrangian as a generalized version of the covariantized Lagrangian for continuum mechanics. We study the cases of 3+1 and 2+1 dimensions and show for the solutions we propose, the Hamiltonian constraint becomes the real homogeneous Monge-Ampere equation in the special case of two spatial dimensions.
