A Classification of Spherically Symmetric Kinematic Self-Similar Perfect-Fluid Solutions

Abstract

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.

Revised version, a reference added, 36 pages, 4 tables, no figures, accepted for publication in Progress of Theoretical Physics

References in corpus (2)

• Gravitational collapse of spherically symmetric perfect fluid with kinematic self-similarity
• Infinite Kinematic Self-Similarity and Perfect Fluid Spacetimes

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