zbMATH — the first resource for mathematics

Type-N, shear-free, perfect-fluid spacetimes with a barotropic equation of state. (English) Zbl 0657.53046
We present the class of Petrov-type N, shear-free, perfect-fluid solutions of Einstein’s field equations in which the fluid satisfies a barotropic equation of state \(p=p(w)\) and \(w+p/0\). All solutions are stationary and possess a three-parameter, abelian group of local isometries which act simply transitively on timelike hypersurfaces. Furthermore, there exists one Killing vector parallel to the vorticity vector and another parallel to the four-velocity. This class of solutions is identified as part of a larger class present in the literature.

53B50 Applications of local differential geometry to the sciences
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
Full Text: DOI
[1] Carminati, J. (1987).J. Math. Phys.,28, 1848. · Zbl 0633.76132
[2] Collins, C. B. (1986).Can. J. Phys.,64, 191.
[3] Lang, J. M., and Collins, C. B. (1987). ?Observationally Homogeneous, Shear-Free Perfect Fluids,? preprint (University of Waterloo, Ontario, Canada). · Zbl 0664.76158
[4] Collins, C. B. (1987). ?Homogeneous and Hypersurface-Homogeneous, Shear-Free Perfect Fluids in General Relativity,? preprint (University of Waterloo, Ontario, Canada).
[5] Krasinski, A. (1978).Rep. Math. Phys.,14, 225. · Zbl 0427.76099
[6] Newman, E. T., and Penrose, R. (1962).J. Math. Phys.,3, 566. · Zbl 0108.40905
[7] Flanders, H. (1963).Differential Forms with Applications to the Physical Sciences (Academic Press, New York). · Zbl 0112.32003
[8] Kramer, D., Stephani, H., MacCallum, M., and Herlt, E. (1980).Exact Solutions of Einstein’s Field Equations (Cambridge University Press, Cambridge, England). · Zbl 0449.53018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.