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A duality relation for fluid spacetime

Naresh Dadhich·L. K. Patel·Ramesh Tikekar
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Abstract

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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Naresh Dadhich, L. K. Patel, Ramesh Tikekar. 1998-01-22. A duality relation for fluid spacetime. https://doi.org/10.1088/0264-9381%2F15%2F4%2F001

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