A vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary spacetimes
Dec 5, 2016Citations per year
Abstract: (arXiv)
We present a new vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes. Specifically, we derive a new hierarchy of higher-order weighted energy estimates by employing appropriate commutator vector fields. In cases where an integrated local energy decay estimate holds, like in the case of sub-extremal Reissner-Nordstrom black holes, this hierarchy leads to almost-sharp global energy and pointwise time-decay estimates with decay rates that go beyond those obtained by the traditional vector field method. Our estimates play a fundamental role in our companion paper where precise late-time asymptotics are obtained for linear scalar fields on such backgrounds.Note:
- 104 pages, 7 figures
References(73)
Figures(7)
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