Phase space analysis on some black hole manifolds

P. Blue, A. Soffer

Research output: Contribution to journalArticlepeer-review

Abstract

The Schwarzschild and Reissner-Nordstrom solutions to Einstein's equations describe space-times which contain spherically symmetric black holes. We consider solutions to the linear wave equation in the exterior of a fixed black hole space-time of this type. We show that for solutions with initial data which decay at infinity and at the bifurcation sphere, a weighted L-6 norm in space decays like t(-1/3). This weight vanishes at the event horizon, but not at infinity. To obtain this control, we require only an is an element of loss of angular derivatives. (C) 2008 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)190
Number of pages90
JournalJournal of functional analysis
Volume256
Issue number1
Early online date10 Nov 2005
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Black holes
  • Phase space analysis
  • Schwarzschild metric
  • Decay estimates
  • KLEIN-GORDON EQUATION
  • SEMILINEAR WAVE-EQUATION
  • ASYMPTOTIC COMPLETENESS
  • BODY PROBLEM
  • SCHWARZSCHILD
  • STABILITY
  • GEOMETRY
  • SCATTERING
  • DECAY
  • SINGULARITY

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