No Access

A NOTE ON THE COLLAPSE OF SMALL DATA SELF-GRAVITATING MASSLESS COLLISIONLESS MATTER

MIHALIS DAFERMOS

Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK

Search for more papers by this author

https://doi.org/10.1142/S0219891606000926Cited by:23 (Source: Crossref)

Abstract

In this note, we show that small-data asymptotically flat spherically-symmetric solutions to the Einstein–Vlasov system for massless particles are causally geodesically complete and decay appropriately. This extends previous results of Rein and Rendall in the massive case.

Keywords:

AMSC: 83C05

References

H. Andréasson, Living Rev. Relativity (2005). Google Scholar
K. Anguige and K. P. Tod, Ann. Phys. 276(2), 294 (1999), DOI: 10.1006/aphy.1999.5947. Crossref, Web of Science, Google Scholar
Y. Choquet-Bruhat, Ann. Inst. Fourier 21, 181 (1971). Crossref, Web of Science, Google Scholar
D. Christodoulou, Class. Quant. Grav. 16, A23 (1999), DOI: 10.1088/0264-9381/16/12A/302. Crossref, Web of Science, Google Scholar
D. Christodoulou and S. Klainerman , The Global Nonlinear Stability of the Minkowski Space , Princeton Mathematical Series 41 ( Princeton University Press , 1993 ) . Google Scholar
M. Dafermos, Class. Quant. Grav. 22, 2221 (2005), DOI: 10.1088/0264-9381/22/11/019. Crossref, Web of Science, Google Scholar
M. Dafermos and A. D. Rendall, An extension principle for the Einstein-Vlasov equations in spherical symmetry, to appear in Ann. Henri Poincaré . Google Scholar
S. W. Hawking and G. F. R. Ellis , The Large Scale Structure of Space-Time , Cambridge Monographs on Mathematical Physics 1 ( Cambridge University Press , 1973 ) . Crossref, Google Scholar
J. M. Martín-García and C. Gundlach, Phys. Rev. D 65, 094026 (2002). Google Scholar
G. Rein and A. D. Rendall, Commun. Math. Phys. 150, 561 (1992), DOI: 10.1007/BF02096962. Crossref, Web of Science, Google Scholar
A. D. Rendall, The Einstein Equations and the Large Scale Behavior of Gravitational Fields (Birkhäuser, Basel, 2004) pp. 231–250. Crossref, Google Scholar