denotes the relativistic velocity of a particle with momentum . The mass of each particle, the
gravitational constant, and the speed of light are all normalized to one. A solution
of this
system is interpreted as follows. The spacetime is a Lorentzian manifold with a conformally-flat
metric
The particle distribution defined on the mass shell in this metric is given by
The Cauchy problem was studied by several authors [51, 50, 15, 108, 131] and the question of global existence of classical solutions for general initial data was open for some time. The problem was given an affirmative solution in 2006 by Calogero [45]. Another interesting result for the Nordström–Vlasov system is given in [36], where a radiation formula, similar to the dipole formula in electrodynamics, is rigorously derived.
http://www.livingreviews.org/lrr-2011-4 |
Living Rev. Relativity 14, (2011), 4
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