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Proof of the Einstein quadrupole formula for solutions of the Einstein–Vlasov system close to Minkowski spacetime

Volume 597 / 2024

Érik Amorim, Håkan Andréasson, Markus Kunze Dissertationes Mathematicae 597 (2024), 93 pp. MSC: Primary 83C35; Secondary 83C05. DOI: 10.4064/dm231107-31-8 Published online: 27 September 2024

Abstract

We rigorously derive the quadrupole formula within the context of the Einstein–Vlasov system. The main contribution of this work is an estimate of the remainder terms, derived from well-defined assumptions, with explicitly stated error terms that depend on the solution’s boundedness and decay properties, and the distance to the source. The assumptions are linked to established properties of global solutions of the Einstein–Vlasov system as in Lindblad and Taylor (2020). Prior derivations of the quadrupole formula have relied on post-Newtonian analysis and lacked comparisons with global solution properties. The importance of the no-incoming-radiation condition is emphasized underscoring the need for solutions satisfying this condition. This work thus addresses the limitations of existing results and provides motivation for further research on global solution properties of the Einstein–Vlasov system.

Authors

  • Érik AmorimMathematisches Institut
    Universität Köln
    D-50931 Köln, Germany
    e-mail
  • Håkan AndréassonMathematical Sciences
    Chalmers University of Technology
    Göteborg University
    S-41296 Göteborg, Sweden
    e-mail
  • Markus KunzeMathematisches Institut
    Universität Köln
    D-50931 Köln, Germany
    e-mail

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