Evolving Lorentzian wormholes supported by phantom matter with constant state parameters

Abstract

In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made out of phantom energy. We show that this exotic source can support the existence of evolving wormhole spacetimes. Explicitly, a family of evolving Lorentzian wormholes conformally related to another family of zero-tidal force static wormhole geometries is found in Einstein gravity. Contrary to the standard wormhole approach, where first a convenient geometry is fixed and then the matter distribution is derived, we follow the conventional approach for finding solutions in theoretical cosmology. We derive an analytical evolving wormhole geometry by supposing that the radial tension (which is negative to the radial pressure) and the pressure measured in the tangential directions have barotropic equations of state with constant state parameters. At spatial infinity this evolving wormhole, supported by this anisotropic matter, is asymptotically flat, and its slices t = constant are spaces of constant curvature. During its evolution the shape of the wormhole expands with constant velocity, i.e without acceleration or deceleration, since the scale factor has strictly a linear evolution.

Two-fluid evolving Lorentzian wormholes

“…Notice that for an anisotropic matter with ω r < −1 we have that ρ in (t, r) > 0, while for an anisotropic matter with ω r > 0 we have that ρ in (t, r) < 0. For ρ(t) = Λ = 0 the shape of the wormhole expands with constant velocity [11]. In the presence of a cosmological constant with ρ in (t, r) = 0 the wormhole configurations have an accelerated expansion (contraction) [12].…”

“…Notice that if ρ(t) = Λ = 0 the space expands with constant velocity [11], and for ρ(t) = 0 and Λ = 0 the rate of expansion is determined by the cosmological constant [12].…”

“…Notice that the field equations (3)- (6) generalize the Einstein equations considered in Refs. [11] and [12]. Thus, in order to quickly solve the field equations we shall use the conservation equations T µ ν;µ = 0.…”

Generalized Second Law of Thermodynamics of Evolving Wormhole with Entropy Corrections

“…The functions b(r) and Φ(t, r) are called the shape function and redshift function respectively. Earlier the evolving wormholes have been studied with time-independent redshift function Φ(r) [29]. If a(t) → constant and Φ(t, r) → Φ(r), then the static MT wormhole can be obtained whereas for b(r) → kr 3 and Φ(t, r) → constant, Eq (1) reduces to standard FRW metric.…”

“…Arellano & Lobo [27] found contracting wormhole solutions within non-linear electrodynamics. Cataldo et al discussed the construction of evolving wormholes using phantom energy [28,29] and more recently using the cosmological constant [30]. Farooq et al [31] showed that the field equations of a (2+1)-dimensional evolving wormhole can be recast into first law of thermodynamics.…”