Abstract
We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions f(R), F(R) and τ0(R), where R is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic (f>0), parabolic (f=0) and elliptic (f<0) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus, if such a dust cloud is placed between two empty (Reissner–Nordström or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics.
Highlights
A wormhole is a kind of spatial geometry resembling a tunnel that connects two different regions of the same space-time, or two different space-times
We study the possible existence of traversable wormholes in general relativity (GR) with another classical and nonexotic form of matter, widely used in various problems of astrophysics and cosmology, namely, dustlike matter, with or without an electromagnetic field
In our recent work [56], we constructed collapsing dusty wormhole solutions using a special choice of arbitrary functions in Tolman’s solution; the internal wormhole solution was matched to external Schwarzschild space-time regions
Summary
A wormhole is a kind of spatial geometry resembling a tunnel that connects two different regions of the same space-time, or two different space-times. In [24], it was shown that static, spherically symmetric wormholes with two flat or AdS asymptotic regions cannot exist in GR with any source matter with isotropic pressure, all such perfect-fluid wormholes contain their exotic sources only in a bounded region, surrounded by vacuum, with thin shells on the boundaries In this connection, we should mention a large class of wormhole models built completely using the thin-shell formalism, where the whole amount of exotic matter is concentrated on a thin shell; among them, Refs. Dynamic wormholes can avoid NEC violation, at least in cases where a static earlytime or late-time asymptotic behavior is absent Such wormhole models with cosmologicaltype metrics are known, for example, in GR with electromagnetic fields described by some special forms of nonlinear electrodynamics [48,49].
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