Establishes tame weighted Sobolev estimates for linear waves on dynamical asymptotically flat spacetimes settling to Kerr, handling zero-energy bound states via microlocal and energy methods to enable nonlinear global existence results.
Radiation field for Einstein vacuum equations with spacial dimension $n\geq 4$
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abstract
In this paper, the radiation field is defined for solutions to Einstein vacuum equations which are close to Minkowski space-time with spacial dimension $n\geq 4$. The regularity properties and asymptotic behavior of those Einstein vacuum solutions are established at the same time. In particular, the map from Cauchy intial data to the radiation field is proved to be an isomorphism when restricting to a small neighborhood of Minkowski data in suitable weighted b-Sobolev spaces.
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math.AP 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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(Non-)Linear waves on asymptotically flat spacetimes. II: trapping, bound states, nonlinear applications
Establishes tame weighted Sobolev estimates for linear waves on dynamical asymptotically flat spacetimes settling to Kerr, handling zero-energy bound states via microlocal and energy methods to enable nonlinear global existence results.