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It is well known that static wormhole configurations in general relativity (GR) are possible only if matter threading the wormhole throat is &ldquo, exotic&rdquo, &mdash, i.e., violates a number of energy conditions. For this reason, it is impossible to construct static wormholes supported only by dust-like matter which satisfies all usual energy conditions. However, this is not the case for non-static configurations. In 1934, Tolman found a general solution describing the evolution of a spherical dust shell in GR. In this particular case, Tolman&rsquo, s solution describes the collapsing dust ball, the inner space-time structure of the ball corresponds to the Friedmann universe filled by a dust. In the present work we use the general Tolman&rsquo, s solution in order to construct a dynamic spherically symmetric wormhole solution in GR with dust-like matter. The solution constructed represents the collapsing dust ball with the inner wormhole space-time structure. It is worth noting that, with the dust-like matter, the ball is made of satisfies the usual energy conditions and cannot prevent the collapse. We discuss in detail the properties of the collapsing dust wormhole.

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&gt, 0), parabolic (f=0) and elliptic (f&lt, 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.

We construct a model of a rotating wormhole made by cutting and pasting two Kerr spacetimes. As a result, we obtain a rotating thin-shell wormhole with exotic matter at the throat. Two candidates for the exotic matter are considered: (i) a perfect fluid; (ii) an anisotropic fluid. We show that a perfect fluid is unable to support a rotating thin-shall wormhole. On the contrary, the anisotropic fluid with the negative energy density can be a source for such a geometry., 8 pages, 3 figures, accepted for publication in Gravitation and Cosmology

We discuss a solution describing a rotating wormhole in general relativity with a scalar field source having negative kinetic energy. To solve the problem, we use the assumption of slow rotation. The role of a small dimensionless parameter is played the ratio of the linear velocity of rotation of the wormhole throat and the velocity of light. The rotating wormhole solution is constructed in the first-order approximation with respect to the small parameter. We analyze the solution obtained and study test particle motion and light propagation in the spacetime of a rotating wormhole.

In 1921 Bach and Weyl derived the method of superposition to construct new axially symmetric vacuum solutions of General Relativity. In this paper we extend the Bach-Weyl approach to non-vacuum configurations with massless scalar fields. Considering a phantom scalar field with the negative kinetic energy, we construct a multi-wormhole solution describing an axially symmetric superposition of $N$ wormholes. The solution found is static, everywhere regular and has no event horizons. These features drastically tell the multi-wormhole configuration from other axially symmetric vacuum solutions which inevitably contain gravitationally inert singular structures, such as `struts' and `membranes', that keep the two bodies apart making a stable configuration. However, the multi-wormholes are static without any singular struts. Instead, the stationarity of the multi-wormhole configuration is provided by the phantom scalar field with the negative kinetic energy. Anther unusual property is that the multi-wormhole spacetime has a complicated topological structure. Namely, in the spacetime there exist $2^N$ asymptotically flat regions connected by throats., 11 pages, 13 figures

We discuss a solution describing a rotating wormhole in the theory of gravity with a scalar field with negative kinetic energy. To solve the problem we use the assumption about slow rotation. The role of a small dimensionless parameter plays the ratio of the linear velocity of rotation of the wormhole's throat and the velocity of light. The rotating wormhole solution is constructed in the framework of the first order approximation with respect to the small parameter. We analyze the obtained solution and study the motion of test particles and the propagation of light in the spacetime of rotating wormhole.

We discuss rotating wormholes in general relativity with a scalar field with negative kinetic energy. To solve the problem, we use the assumption about slow rotation. The role of a small dimensionless parameter plays the ratio of the linear velocity of rotation of the wormhole's throat and the velocity of light. We construct the rotating wormhole solution in the second order approximation with respect to the small parameter. The analysis shows that the asymptotical mass of the rotating wormhole is greater than that of the non-rotating one, and the NEC violation in the rotating wormhole spacetime is weaker than that in the non-rotating one., Comment: 12 pages, 9 figures, appeared in PRD