New asymptotically flat phantom wormhole solutions

Abstract

A possible cause of the late-time cosmic acceleration is an exotic fluid with an equation of state lying within the phantom regime, i.e., $w=p/\rho <-1$. The latter violates the null energy condition, which is a fundamental ingredient in wormhole physics. Thus, cosmic phantom energy may, in principle, provide a natural fluid to support wormholes. In this work, we find new asymptotically flat wormhole solutions supported by the phantom energy equation of state, consequently extending previous solutions. Thus, there is no need to surgically paste the interior wormhole geometry to an exterior vacuum spacetime. In the first example, we carefully construct a specific shape function, where the energy density and pressures vanish at large distances as $\sim 1/r^n$, with $n>0$. We also consider the "volume integral quantifier", which provides useful information regarding the total amount of energy condition violating matter, and show that, in principle, it is possible to construct asymptotically flat wormhole solutions with an arbitrary small amount of energy condition violating matter. In the second example, we analyse two equations of state, i.e., $p_r=p_r(\rho )$ and $p_t=p_t(\rho )$, where we consider a specific integrability condition in order to obtain exact asymptotically flat wormhole solutions. In the final example, we postulate a smooth energy density profile, possessing a maximum at the throat and vanishing at spatial infinity.

7 pages, 2 figures. V2: 11 pages, 6 figures; two new solutions, stability discussion and references added; to appear in PRD. V3: typos corrected

References in corpus (19)

• Can dark energy evolve to the Phantom?
• Wormhole geometries in f(R) modified theories of gravity
• Wormholes supported by hybrid metric-Palatini gravity
• Thin accretion disks in stationary axisymmetric wormhole spacetimes
• Wormhole geometries supported by a nonminimal curvature-matter coupling
• Nonminimal curvature-matter coupled wormholes with matter satisfying the null energy condition
• Instability of wormholes supported by a ghost scalar field. I. Linear stability analysis
• Plane symmetric thin-shell wormholes: solutions and stability
• Electromagnetic signatures of thin accretion disks in wormhole geometries
• A general class of braneworld wormholes
• General class of wormhole geometries in conformal Weyl gravity
• Instability of wormholes supported by a ghost scalar field. II. Nonlinear evolution
• No realistic wormholes from ghost-free scalar-tensor phantom dark energy
• Self sustained phantom wormholes in semi-classical gravity
• Phantom stars and topology change
• Self-sustained traversable wormholes in noncommutative geometry
• Van der Waals quintessence stars
• Scalar wormholes in cosmological setting and their instability
• Networks of cosmological histories, crossing of the phantom divide line and potentials with cusps