Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-07-30
Prog.Theor.Phys. 108 (2002) 819-851
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Revised version, a reference added, 36 pages, 4 tables, no figures, accepted for publication in Progress of Theoretical Physic
Scientific paper
10.1143/PTP.108.819
We classify all spherically symmetric spacetimes admitting a kinematic self-similar vector of the second, zeroth or infinite kind. We assume that the perfect fluid obeys either a polytropic equation of state or an equation of state of the form $p=K\mu$, where $p$ and $\mu$ are the pressure and the energy density, respectively, and $K$ is a constant. We study the cases in which the kinematic self-similar vector is not only ``tilted'' but also parallel or orthogonal to the fluid flow. We find that, in contrast to Newtonian gravity, the polytropic perfect-fluid solutions compatible with the kinematic self-similarity are the Friedmann-Robertson-Walker solution and general static solutions. We find three new exact solutions which we call the dynamical solutions (A) and (B) and $\Lambda$-cylinder solution, respectively.
Harada Tomohiro
Iguchi Hideo
Maeda Hideki
Okuyama Naoya
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