论文标题
关于爱因斯坦歧管上的线性真空约束方程
On linearised vacuum constraint equations on Einstein manifolds
论文作者
论文摘要
我们展示了如何通过不受限制的电位参数化一般相对论矢量约束方程的解决方案。我们为满足线性化标量约束的张量的无痕迹部分提供了类似的结构。在宇宙常数$λ$为零的情况下，我们的先前工作为线性约束的解决方案提供了类似的不同构造。我们使用新电位来证明可以使用线性化的引力场来屏蔽线性化的引力场而不施加TT量规（如先前的工作中所做的那样），以任何$λ\ in \ Mathbb {r} $的任何值。
We show how to parameterise solutions of the general relativistic vector constraint equation on Einstein manifolds by unconstrained potentials. We provide a similar construction for the trace-free part of tensors satisfying the linearised scalar constraint. Previous work of ours has provided similar different constructions for solutions of the linearized constraints in the case where the cosmological constant $Λ$ is zero. We use our new potentials to show that one can shield linearised gravitational fields using linearised gravitational fields without imposing the TT gauge (as done in previous work), for any value of $Λ\in \mathbb{R}$.
