1996
DOI: 10.1088/0264-9381/13/7/014
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Shear-free perfect fluids in general relativity: III. Petrov type III spacetimes

Abstract: It is shown that for any Petrov type III, shear-free, perfect fluid solution of Einstein's field equations, in which the perfect fluid satisfies a barotropic equation of state p = p(w) such that , the fluid volume expansion is zero, or the equation of state satisfies . It follows that all such perfect fluids whose equation of state is the gamma law, must have zero fluid volume expansion.

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Cited by 10 publications
(11 citation statements)
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“…ix. Finally, there are some recent partial results on Petrov type III by Carminati [5] and by Carminati and Cyganowski [6].…”
Section: Introductionmentioning
confidence: 94%
“…ix. Finally, there are some recent partial results on Petrov type III by Carminati [5] and by Carminati and Cyganowski [6].…”
Section: Introductionmentioning
confidence: 94%
“…(viii) For the fluid velocity parallel to a conformal Killing vector field (Coley [25]). (ix) Petrov type III (Carminati [26] and Carminati and Cyganowski [27,28]).…”
Section: F Sopuertamentioning
confidence: 99%
“…where θ is the fluid's (rate of volume) expansion, ua is the acceleration and σ ab , ω ab are respectively the shear and vorticity tensors, which are uniquely defined by (3) and the properties u a ua = 0, u a ω ab = u a σ ab = 0, σ [ab] = ω (ab) = 0, σ a a = 0.…”
Section: Introductionmentioning
confidence: 99%
“…( ) q q w = [32]; Petrov types N [2] and III [3,4]; the existence of a conformal Killing vector parallel to the fluid flow [9]; the Weyl tensor having either a divergence-free electric part [39], or a divergence-free magnetic part, in combination with an equation of state which is of the γ-law type [38] or which is sufficiently generic [5], and in the case where the Einstein field equations are linearised about a FLRW background [25] . A major step has been achieved recently by the second author [30] proving the conjecture for an arbitrary γ-law equation of state (except for the cases…”
mentioning
confidence: 99%