Abstract
Traversability in relation with tides across thin-shell wormholes is analyzed. Conditions for a safe travel through a wormhole throat are established in terms of the parameters characterizing the geometries and reasonable assumptions regarding the travellers motion. Most convenient geometries turn to include the physically interesting example of wormholes connecting locally flat submanifolds as those associated to gauge cosmic strings. A certain relaxation of the conditions imposed and the corresponding extension of the set of admissible configurations is also briefly discussed.
Highlights
In principle we would not be worried a e-mail: erdec@df.uba.ar b e-mail: csimeone@df.uba.ar about what happens between two points of an object while both of them are at the same side of a wormhole throat, but by the possibility of great tensions acting on an object traveling across the throat, that is where problems associated with curvature can manifest
A reasonable condition to consider the latter would be to have a finite quotient between the tidal acceleration and the separation of the two points. This seems to point out that whenever an infinitely thin matter layer is present, traversability in this sense would be in trouble, as a thin-shell is associated to a discontinuity in the extrinsic curvature, which is the covariant form of the discontinuity of the first derivatives of the metric; this seems to exclude a finite limit for the quotient a/ x for two infinitely close points, one at each side of the shell
We study tides oven an object at rest with a coordinate extension r = (η) r+ + (−η) r− transverse to the throat; we have to compute the relative acceleration between two points on the same radial direction with separation vector given by ( x)μ = r δr μ
Summary
A reasonable condition to consider the latter would be to have a finite quotient between the tidal acceleration and the separation of the two points. We will begin by studying two close points of an object, one at each side of the throat, and both in the same radial direction of the geometry considered. We will treat the case of two close points separated over a transverse direction parallel to the throat, focusing on the possible problems which appear when the object crosses the throat surface. J. C (2021) 81:937 present metric coefficients −g00 = gzz = 1 (see below) and tides in the radial direction and in the direction parallel to the symmetry axis are not a problem; for points along the angular direction, even for such backgrounds, the mere possibility of safe tides demands, in addition, a small speed. A further analysis will be briefly performed about some possible relaxation of both the conditions imposed on the geometries connected by the throat, and on the idealized infinitely-thin layer model of the matter on this surface
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