23 research outputs found
Local energy estimate on Kerr black hole backgrounds
We study dispersive properties for the wave equation in the Kerr space-time
with small angular momentum. The main result of thispaper is to establish
uniform energy bounds and local energy decay for such backgrounds.Comment: 26 page
Pointwise decay for the Maxwell field on black hole space-times
In this article we study the pointwise decay properties of solutions to the
Maxwell system on a class of nonstationary asymptotically flat backgrounds in
three space dimensions. Under the assumption that uniform energy bounds and a
weak form of local energy decay hold forward in time, we establish peeling
estimates for all the components of the Maxwell tensor.Comment: 34 pages, several typos corrected and proofs expande
Pointwise decay for the Maxwell field on black hole space–times
Abstract In this article we study the pointwise decay properties of solutions to the Maxwell system on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time, we establish peeling estimates, as well as a t−4 rate of decay on compact regions for all the components of the Maxwell tensor
Price's Law on Nonstationary Spacetimes
In this article we study the pointwise decay properties of solutions to the
wave equation on a class of nonstationary asymptotically flat backgrounds in
three space dimensions. Under the assumption that uniform energy bounds and a
weak form of local energy decay hold forward in time we establish a
local uniform decay rate (Price's law \cite{MR0376103}) for linear waves. As a
corollary, we also prove Price's law for certain small perturbations of the
Kerr metric.
This result was previously established by the second author in \cite{Tat} on
stationary backgrounds. The present work was motivated by the problem of
nonlinear stability of the Kerr/Schwarzschild solutions for the vacuum Einstein
equations, which seems to require a more robust approach to proving linear
decay estimates.Comment: 32 pages, no figures, typos correcte
Strichartz estimates on Schwarzschild black hole backgrounds
We study dispersive properties for the wave equation in the Schwarzschild
space-time. The first result we obtain is a local energy estimate. This is then
used, following the spirit of earlier work of Metcalfe-Tataru, in order to
establish global-in-time Strichartz estimates. A considerable part of the paper
is devoted to a precise analysis of solutions near the trapping region, namely
the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place