A Vector Field Method for Radiating Black Hole Spacetimes

Abstract

We develop a commuting vector field method for a general class of radiating spacetimes. The metrics considered are certain long range perturbations of Minkowski space including those constructed from global stability problems in general relativity. Our method provides sharp peeling estimates for solutions to both linear and nonlinear (null form) scalar fields.

References in corpus (1)

• On the asymptotic behavior of solutions to Einstein's vacuum equations in wave coordinates

Cited by in corpus (6)

• The non-linear stability of the Schwarzschild family of black holes
• Pointwise decay for the wave equation on nonstationary spacetimes
• A local energy estimate for wave equations on metrics asymptotically close to Kerr
• Pointwise decay for semilinear wave equations on Kerr spacetimes
• A Sufficient Condition for Blowup of the Nonlinear Klein-Gordon Equation with Positive Initial Energy in FLRW Spacetimes
• Semilinear wave equations on accelerated expanding FLRW spacetimes