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

Onyx Gautam

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arXiv · 2605.03220

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

Onyx Gautam

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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.

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Onyx Gautam. 2026-05-04. Late-time tails for linear waves on radially symmetric stationary spacetimes of two space dimensions. https://arxiv.org/abs/2605.03220

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