Vol. 13, No. 1, 2020

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A vector field method for radiating black hole spacetimes

Jesús Oliver and Jacob Sterbenz

Vol. 13 (2020), No. 1, 29–92
Abstract

We develop a commuting vector field method for a general class of radiating spacetimes. The metrics we consider are modeled on those constructed from global nonlinear stability problems in general relativity, and our method provides sharp peeling estimates for solutions to both linear and (null form) nonlinear scalar fields.

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Keywords
wave equation, local energy decay, vector field method
Mathematical Subject Classification 2010
Primary: 35L10
Milestones
Received: 30 May 2017
Revised: 24 September 2018
Accepted: 29 December 2018
Published: 6 January 2020
Authors
Jesús Oliver
Department of Mathematics
California State University, East Bay
Hayward, CA
United States
Jacob Sterbenz
Department of Mathematics
University of California at San Diego
La Jolla, CA
United States