Geodesics and the Einstein nonlinear wave system
| Autor: | David M. A. Stuart |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Mathematics(all)
Geodesic Einstein's constant Applied Mathematics General Mathematics Mathematical analysis Wave equation Solitons Sobolev space symbols.namesake Scaling limit Minkowski space symbols Nonlinear wave equations on manifolds Soliton Einstein Godesic Nonlinear Sciences::Pattern Formation and Solitons Mathematics |
| Zdroj: | Journal de Mathématiques Pures et Appliquées. 83:541-587 |
| ISSN: | 0021-7824 |
| DOI: | 10.1016/j.matpur.2003.09.009 |
| Popis: | The system under consideration is Einstein's equation Rμν(g)−gμνR(g)/2=8πGTμν for a pseudo-Riemannian metric g coupled to a semi-linear wave equation for a complex function φ. Assume that this wave equation on Minkowski space admits a stable solitary wave of the type known as nontopological solitons. The system is studied in the scaling limit in which the solitons have small size e and amplitude δ with δ⩽δ0e7/4. It is proved that, for e sufficiently small, given a solution of the vacuum Einstein equation, i.e., a Ricci flat pseudo-Riemannian metric γ, there exists a finite time interval, independent of e,δ, on which there is a solution of the full system (g,φ) with (g−γ) small and φ close to a nontopological soliton centred on a time-like geodesic (in appropriate Sobolev norms). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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