Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-01-20
Class.Quant.Grav.11:3049-3068,1994
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex, no figures
Scientific paper
10.1088/0264-9381/11/12/018
Stationary and axisymmetric perfect-fluid metrics are studied under the assumption of the existence of a conformal Killing vector field and in the general case of differential rotation. The possible Lie algebras for the conformal group and corresponding canonical line-elements are explicitly given. It turns out that only four different cases appear, the abelian and other three called I, II and III. We explicitly find all the solutions in the abelian and I cases. For the abelian case the general solution depends on an arbitrary function of a single variable and the perfect fluid satisfies the equation of state rho = p+const. This class of metrics is the one presented recently by one of us. The general solution for case I is a new Petrov type D metric, with the velocity vector outside the 2-space spanned by the two principal null directions and a barotropic equation of state rho +3p=0. For the cases II and III, the general solution has been found only under the further assumption of a natural separation of variables Ansatz. The conformal Killing vectors in the solutions that come out here are, in fact, homothetic. No barotropic equation of state exists in these metrics unless for a new Petrov type D solution belonging to case II and with rho +3p=0 which cannot be interpreted as an axially symmetric solution and such that the velocity vector points in the direction of one of the Killing vectors. This solution has the previously unknown curious property that both commuting Killing vectors are timelike everywhere.
Mars Marc
Senovilla José M. M.
No associations
LandOfFree
Stationary and Axisymmetric Perfect-Fluid Solutions with Conformal Motion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stationary and Axisymmetric Perfect-Fluid Solutions with Conformal Motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stationary and Axisymmetric Perfect-Fluid Solutions with Conformal Motion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-665969