Conformal-symmetry Wormholes Supported by a Perfect Fluid

Abstract

This paper presents a new wormhole solution by assuming that a homogeneously distributed fluid with equation of state $p=\omega\rho$ can be adapted to an anisotropic spacetime such as a wormhole and that this spacetime admits a one-parameter group of conformal motions. The pressure $p$ in the equation of state becomes the lateral pressure $p_t$ instead of the radial pressure $p_r$, as assumed in previous studies. Given that $p_t=\omega\rho$, $p_r$ is then determined from the Einstein field equations. A wormhole solution can be obtained only if $\omega <-1$ or $0<\omega <1$. Since the former case corresponds to phantom dark energy, which has been the subject of earlier studies, we concentrate mainly on the latter. This case implies that given the above conditions, dark matter can support traversable wormholes.