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General Relativity and Gravitation

, Volume 18, Issue 6, pp 649–668 | Cite as

Irrotational and conformally Ricci-flat perfect fluids

  • N. Van den Bergh
Research Articles

Abstract

When a space-time, containing an irrotational perfect fluid withw + p ≠ 0, is conformally Ricci-flat, three possibilities arise: (a) When the gradient of the conformal scalar field is aligned with the fluid velocity, the solution is conformally flat; (b) when the gradient is orthogonal to the fluid velocity, solutions are either shearfree, nonexpanding and (pseudo-) spherically or plane-symmetric, or they are conformally related to a particular new vacuum solution admitting a three-dimensional group of motions of Bianchi type VIo on a timelike hypersurface; (c) in the general case solutions are (pseudo) spherically or plane-symmetric and have nonvanishing expansion.

Keywords

Scalar Field Differential Geometry Fluid Velocity Perfect Fluid Bianchi Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Van den Bergh, N. (1985). Conformally Ricci-Flat Perfect Fluids.J. Math. Phys. (to be published).Google Scholar
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    Van den Bergh, N. (1985). The General Solution for Shearfree and Conformally Ricci-Flat Perfect Fluids.Lett. Math. Phys. (to be published).Google Scholar
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    Barnes, A. (1973).Gen. Rel. Grav.,4, 105.Google Scholar
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    Kramer, D., Stephani, H., MacCallum, M. A. H., and Herlt, E. (1980).Exact Solutions of Einstein's Field Equations (Cambridge University Press, Massachusetts).Google Scholar
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    Kozameh, C. N., Newman, E. T., and Tod, K. P. (1985).Gen. Rel. Grav.,17, 343.Google Scholar
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    Van den Bergh, N., and Wils, P. (1985).Gen. Rel. Grav.,17, 223.Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • N. Van den Bergh
    • 1
    • 2
  1. 1.Theoretical Astronomy Unit, School of Mathematical SciencesQueen Mary CollegeLondonUK
  2. 2.Physics DepartmentUniversitaire Instelling AntwerpenAntwerpenBelgium

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