Phantom evolving wormholes with big rip singularities

Abstract

We investigate a family of inhomogeneous and anisotropic gravitational fields exhibiting a future singularity at a finite value of the proper time. The studied spherically symmetric spacetimes are asymptotically Friedmann-Robertson-Walker at spatial infinity and describe wormhole configurations filled with two matter components: one inhomogeneous and anisotropic fluid and another isotropic and homogeneously distributed fluid, characterized by the supernegative equation of state \omega=p/\rho < -1. In previously constructed wormholes, the notion of the phantom energy was used in a more extended sense than in cosmology, where the phantom energy is considered a homogeneously distributed fluid. Specifically, for some static wormhole geometries the phantom matter was considered as an inhomogeneous and anisotropic fluid, with radial and lateral pressures satisfying the relations $p_{r}/\rho<-1$ and $p_{_l} \neq p_r$, respectively. In this paper we construct phantom evolving wormhole models filled with an isotropic and homogeneous component, described by a barotropic or viscous phantom energy, and ending in a big rip singularity. In two of considered cases the equation of state parameter is constrained to be less than -1, while in the third model the finite-time future singularity may occur for $\omega<-1$, as well as for $-1 < \omega \leq 1$.Comment: 9 pages, 9 figures, accepted for publication in Phys. Rev.