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Conformally Ricci-flat spacetimes admitting a Killing vector field parallel to the gradient of the conformal scalar field

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Abstract

It is shown that the stress-energy tensor of a conformally Ricci-flat spacetime in which there exists a Killing vector field parallel to the gradient of the conformal scalar field (a) cannot be of the perfect fluid type and (b) can only originate in an electromagnetic field when the latter is null and the solution belongs to a particular class of pp-waves.

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References

  1. Kramer, D., Stephani, H., MacCallum, M. A. H., and Herlt, E., Exact Solutions of Einstein's Field Equations, CUP, Cambridge, 1980.

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  2. Van den Bergh, N., ‘Conformally Ricci Flat Perfect Fluids’, J. Math. Phys. (1986) (to be published).

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  4. Van den Bergh, N., ‘Irrotational and Conformally Ricci Flat Perfect Fluids’, Gen. Rel. Grav. (1986) (to be published).

  5. Van den Bergh, N., ‘Conformally Ricci Flat Einstein-Maxwell Fields with a Null Electromagnetic Field’, Gen. Rel. Grav. (1986) (to be published).

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Authors and Affiliations

  1. Theoretical Astronomy Unit, School of Mathematical Sciences, Queen Mary College, London, UK

    N. Van Der Bergh

  2. Physics Department, Universitaire Instelling Antwerpen, Antwerp, Belgium

    N. Van Der Bergh

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  1. N. Van Der Bergh
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Van Der Bergh, N. Conformally Ricci-flat spacetimes admitting a Killing vector field parallel to the gradient of the conformal scalar field. Lett Math Phys 12, 43–47 (1986). https://doi.org/10.1007/BF00400302

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  • DOI: https://doi.org/10.1007/BF00400302

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