论文标题
具有逆方势的几何波方程的迟发时间渐近学
Late-time asymptotics for geometric wave equations with inverse-square potentials
论文作者
论文摘要
我们引入了一种新的基于物理空间的方法，用于在渐近平坦的时空背景上推导解决方案解决方案的精确前阶延迟行为，并将其应用于Schwarzschild黑洞上具有渐近倒数势力的波方程的设置。这提供了一个有用的玩具模型设置，用于引入适用于更通用的线性和非线性几何波动方程，例如电磁电荷标量字段的波程，在极端尺寸的极端kerr黑洞和几何图上的波动方程，即使在现有的延迟时间上不适用空间尺寸的证据，可能无法应用精确的准时。我们介绍的方法依赖于利用解决方案时间积分的空间衰减特性来得出渐近延迟尾巴的存在和精确的通用性能，并在时间上获得尖锐，均匀的衰减估计值。
We introduce a new, physical-space-based method for deriving the precise leading-order late-time behaviour of solutions to geometric wave equations on asymptotically flat spacetime backgrounds and apply it to the setting of wave equations with asymptotically inverse-square potentials on Schwarzschild black holes. This provides a useful toy model setting for introducing methods that are applicable to more general linear and nonlinear geometric wave equations, such as wave equations for electromagnetically charged scalar fields, wave equations on extremal Kerr black holes and geometric wave equations in even space dimensions, where existing proofs for deriving precise late-time asymptotics might not apply. The method we introduce relies on exploiting the spatial decay properties of time integrals of solutions to derive the existence and precise genericity properties of asymptotic late-time tails and obtain sharp, uniform decay estimates in time.
