论文标题
在$ u（1）$对称性中挤压固定量的重力能量
Squeezing a fixed amount of gravitational energy to arbitrarily small scales, in $U(1)$ symmetry
论文作者
论文摘要
我们证明了在极化u（1）对称性中真空爱因斯坦方程的溶液均匀存在，这些对称是在2 + 1个时空中由U（1）对称性获得的2 + 1个时空中支持的均匀阳性$ H^1 $的能量。我们还构建了一个子类的溶液，该溶液在整个演化过程中都保持了能量（沿U（1）家族）的浓缩。这些结果依赖于三个创新：在零地球测量表中的2 + 1爱因斯坦方程，该仪表中爱因斯坦方程的新型抛物面缩放以及新的klainerman-sobolev在矩形条上的不平等。
We prove uniform finite-time existence of solutions to the vacuum Einstein equations in polarized U(1) symmetry which have uniformly positive incoming $H^1$ energy supported on an arbitrarily small set in the 2 + 1 spacetime obtained by quotienting by the U(1) symmetry. We also construct a subclass of solutions for which the energy remains concentrated (along a U(1) family of geodesics) throughout its evolution. These results rely on three innovations: a direct treatment of the 2 + 1 Einstein equations in a null geodesic gauge, a novel parabolic scaling of the Einstein equations in this gauge, and a new Klainerman-Sobolev inequality on rectangular strips.
