An asymptotic analysis of spherically symmetric perfect fluid self-similar solutions

Details An asymptotic analysis of spherically symmetric perfect fluid self-similar solutions An asymptotic analysis of spherically symmetric perfect fluid self-similar solutions

2000-08-01

arxiv.org/abs/gr-qc/0008007v1

Class.Quant.Grav.17:4339-4352,2000

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages. Submitted to Class. Quantum Grav

Scientific paper

10.1088/0264-9381/17/20/309

The asymptotic properties of self-similar spherically symmetric perfect fluid solutions with equation of state p=alpha mu (-1alpha >-1 or asymptotically static for 1>alpha >0. Others are associated with an approximate power-law solution, in which case they are asymptotically quasi-static for 1>alpha >0 or asymptotically Minkowski for 1>alpha >1/5. We also show that there are solutions whose asymptotic behaviour is associated with finite values of z and which depend upon powers of ln z. These correspond either to a second family of asymptotically Minkowski solutions for 1>alpha>1/5 or to solutions that are asymptotically Kasner for 1>alpha>-1/3. There are some other asymptotic power-law solutions associated with negative alpha, but the physical significance of these is unclear. The asymptotic form of the solutions is given in all cases, together with the number of associated parameters.

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