| Abstract: |
| The late-time behavior of the linear Klein-Gordon equation on a Schwarzschild geometry, which models the simplest black hole in General Relativity, has long posed a significant challenge due to the presence of stable (timelike) trapping. We present our recent resolution of this problem, uncovering an unexpected contrast between solutions with exponentially decaying initial data and those with polynomial decay. These results lay the groundwork for future exploration of the nonlinear dynamics of the Schwarzschild black hole for the Einstein-Klein-Gordon equations. |
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