A duality relation for fluid spacetime

We consider the electromagnetic resolution of gravitational field. We show that under the duality transformation, in which active and passive electric parts of the Riemann curvature are interchanged, a fluid spacetime in comoving coordinates remains invariant in its character with density and pressure transforming, while energy flux and anisotropic pressure remaining unaltered. Further if fluid admits a barotropic equation of state, $p = (γ- 1) ρ$ where $1 \leq γ\leq 2$, which will transform to $p = (\frac{2 γ}{3 γ- 2} - 1) ρ$. Clearly the stiff fluid and dust are dual to each-other while $ρ+ 3 p =0$, will go to flat spacetime. However the n $(ρ- 3 p = 0)$ and the deSitter $(ρ+ p = 0$) universes ar e self-dual.

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