Selfsimilar analysis of VlasovEinstein equations in spherical symmetry
Abstract
The VlasovEinstein system of equations is studied from the point of view of group transformations. Continuous groups are shown to generalize the usual infinitesimal treatment of the metric tensor to the case of a distribution function. Reduced equations are obtained, leading to a timedependent analytical solution, which yields as a limiting case the Schwarzschild metric. The problem of a purely radial motion of null particles is discussed and leads to an expression for the redshift in a nonstatic, inhomogeneous spacetime.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 1980
 DOI:
 10.1086/157824
 Bibcode:
 1980ApJ...236..970M
 Keywords:

 Einstein Equations;
 Relativity;
 SpaceTime Functions;
 Transformations (Mathematics);
 Vlasov Equations;
 Cosmology;
 Group Theory;
 Invariance;
 Red Shift;
 Schwarzschild Metric;
 Tensor Analysis;
 Astrophysics