General Relativity and Gravitation

, Volume 24, Issue 6, pp 599–615 | Cite as

Shear-free spherically symmetric perfect fluid solutions with conformal symmetry

  • Peter Havas
Research Articles


In 1987, Dyer, McVittie and Oattes determined the general relativistic field equations for a shear-free perfect fluid with spherical symmetry and a conformal Killing vector in thet-r plane, which depend on an arbitrary constantm. Two particular solutions of these equations were given recently by Maharaj, Leach and Maartens, as well as a partial solution thought to be valid for almost allm. In this paper, this solution is completed for four values ofm, and it is shown that it cannot be completed for any others by currently available techniques; however, a new solution of a different form, but also depending on a Weierstrass elliptic function, is found for a further value ofm. None of these metrics are conformally flat; one of them has a constant expansion rate.


Partial Solution Elliptic Function Expansion Rate Spherical Symmetry Conformal Symmetry 
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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Peter Havas
    • 1
  1. 1.Department of PhysicsTemple UniversityPhiladelphiaUSA

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