Weyl metrics and wormholes

Abstract

Abstract. We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from solutions with locally flat geometry.arXiv:1701.05533v3 [hep-th]

Traversable Schwarzschild-like wormholes

“…The radial tidal constraint can be regarded as constraining the redshift function, while the lateral tidal constraint can be regarded as constraining the speed v with which the traveler crosses the wormhole [1,2]. In the case of zero-tidal-force Schwarzschild-like wormhole (8) we conclude that the radial tidal constraint is everywhere identically zero. On the other hand, for the lateral tidal constraint we obtain γ 2 v 2 2r 3 r 0 (β − 1) |ξ | g ⊕ .…”

“…We have also considered a description of the geodesic behavior for zero-tidal-force Schwarzschild-like wormholes (8), corresponding to different values of the β-parameter. The analysis of the Euler-Lagrange equation shows that a test particle, radially moving toward the throat, always reaches it with a zero velocity at a finite time, while for radial outwards geodesics the particle velocity tends to of maximum value, reaching the infinity.…”

“…Let us now focus to traversability conditions of the zerotidal-force Schwarzschild-like wormhole (8). We shall suppose that a traveler journeys radially through the wormhole (8), beginning at rest in the space station 1 in the lower universe, and ending at rest in a space station 2 in the upper universe.…”

“…Because we deal with spherical metric (8) we shall consider the test particle paths confined to the plane θ = π/2. Therefore we have…”

“…On the other hand, for r 2φ = L the initial conditions imply that for a particle starting to move at r i with initial angular velocityφ i we have r 2 iφ i = L. We shall see later that the presence of the angular momentum L in Eq. (19) allows the β-parameter influences the trajectories of non-circular geodesics of the spacetime (8). For circular geodesics it must be required that its radial velocity vanishes, i.e.…”