A duality relation for fluid spacetime

Details A duality relation for fluid spacetime A duality relation for fluid spacetime

1998-01-22

arxiv.org/abs/gr-qc/9801076v1

Class.Quant.Grav.15:L27-L29,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, LaTeX version, Accepted in Classical Quantum Gravity as a Letter

Scientific paper

10.1088/0264-9381/15/4/001

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, $p = (\gamma - 1) \rho$ where $1 \leq \gamma \leq 2$, which will transform to $p = (\frac{2 \gamma}{3 \gamma - 2} - 1) \rho$. Clearly the stiff fluid and dust are dual to each-other while $\rho + 3 p =0$, will go to flat spacetime. However the n $(\rho - 3 p = 0)$ and the deSitter $(\rho + p = 0$) universes ar e self-dual.

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