A duality relation for fluid spacetime

TL;DR

This paper explores a duality transformation in fluid spacetimes, showing invariance properties and how different fluid states transform under this duality, revealing connections between various cosmological models.

Contribution

It introduces a duality relation for fluid spacetimes that preserves certain characteristics and relates different equations of state, including self-dual universes.

Findings

Fluid spacetime invariance under duality transformation

Transformation of barotropic equation of state parameters

Duality links stiff fluid and dust, and relates de Sitter and flat spacetime

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, $p = (\gamma - 1) \rho$ 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.