Late-time tails for linear waves on radially symmetric stationary spacetimes of two space dimensions

Abstract

We show that the leading-order term in the late-time asymptotics of solutions to the linear wave equation on radially symmetric stationary perturbations of $(2+1)$-dimensional Minkowski space is proportional to $u^{-1/2}{v}^{-1/2}$ (which solves the wave equation on Minkowski space), where $u$ and $v$ are double null coordinates. Our proof adapts the physical space techniques in the work of Gajic (arXiv:2203.15838) on the wave equation with an inverse-square potential on the Schwarzschild spacetime. In particular, we extend the $r^p$-weighted energy estimates of Dafermos--Rodnianski (arXiv:0910.4957) to two space dimensions.

59 pages, 1 figure; corrected typos