Historical research guide · 0721 · 2024
Traversable wormholes induced by stress energy conservation: combining Casimir energy with a scalar field
Remo Garattini · Athanasios G. Tzikas
In one minute
Remo Garattini and Athanasios Tzikas, both at the University of Bergamo, put a concrete engineering question to wormholes. A throat you can actually travel through needs a source whose energy density and pressure add to less than zero, and the one place a laboratory already produces that is the gap between two Casimir plates, where excluding the longest modes leaves the space between them below the ambient vacuum level. Garattini’s earlier Casimir wormhole used that alone. Here the two authors add an ordinary scalar field, once without a potential and once with one, and set the Casimir plates either at a fixed separation or at one that changes with radius — then insist that the total stress-energy be conserved rather than assumed. Conservation turns out to be the hard constraint. In three of the four combinations it forces a further term into the equations, which they read as the wormhole’s own gravitational back-reaction on its source. One combination does not need it: a scalar field carrying potential energy, alongside a Casimir device with fixed plates.
Connection
Chapter 4 needs the wormhole conversation to be a real engineering conversation, and this is what that looks like — a named laboratory effect used as the source term, a conservation law used as the test, and a single surviving configuration named at the end. It also joins chapter 2 to chapter 4 directly: the Casimir gap is the vacuum structure chapter 2 teaches, used here as the material a metric is built from.
From the source
The premise, stated as an experimental fact rather than a hypothesis. A traversable wormhole requires violation of the null energy condition, which means a source whose energy density and radial pressure add to less than zero — what the literature calls exotic matter with negative energy density, and what is better described as sitting below the ambient vacuum level. Garattini and Tzikas anchor that in the Casimir experiment: fewer virtual particles per unit volume in the gap than outside it, the plates attracting as a result, and the authors’ own verdict that the Casimir effect provides real experimental evidence that the energy conditions are occasionally violated by quantum effects.Section I, Introduction, paragraph following equation (7); equation (8) gives the Casimir stress-energy tensor
Adding an ordinary electric field to a Casimir wormhole does not close the throat. Because the electric field’s energy density and radial pressure are equal and opposite, they cancel in the null-energy sum, and the combined source still comes out below zero by exactly the Casimir amount. This is why the authors move to a scalar field, where the cancellation does not happen and the answer is not obvious in advance.Section I, equations (9) to (11)
The construction. The total stress-energy is written as three pieces: the scalar field, the Casimir source, and a third piece the authors introduce only after solving the field equations with the first two. That third piece is deliberately not treated as an unknown matter field; it is read as the gravitational back-reaction of the traversable wormhole to the matter source, and the paper’s interest is in which configurations need it and which do not.Section I, equations (12) to (14)
Four configurations were tested — a massless scalar field with no potential and a massive one with a potential, each combined with Casimir plates held at a fixed separation and with plates whose separation varies with radius. A solution appears in every profile. Every one of them must be confined to a bounded region to keep the redshift or shape function from diverging, so the model is not asymptotically flat; the authors propose closing that gap by gluing the inner throat to flat Minkowski space with thin-shell junction techniques, and name it as future work.Sections II and III; conclusions in Section IV
The result the paper is for. Only one of the four combinations avoids the extra back-reaction term altogether — a scalar field with a potential, alongside a Casimir device with fixed plates. The authors mark it in their own words as the only case in which the wormhole stress-energy tensor does not come into play. The geometry that survives there is close to what the literature calls an absurdly benign traversable wormhole: a shape function that switches off at an outer boundary sitting at twice the throat radius, with the flaring-out condition satisfied throughout.Section III A, equations (108) to (120); the quoted line follows equation (120)
What to watch, and the authors flag it themselves. In the case without a potential the predicted throat comes out enormous — proportional to the plate separation squared divided by the Casimir length scale, about 1.7 times ten to the seventeenth metres, some eighteen light-years across. Their closing sentence is that at this stage of their research they are unaware of the reasons behind this result. Understanding what sets that scale, and whether the potential-carrying case brings it down, is the next thing to follow in this line of work.Section IV, Conclusions, final paragraph
The way in
https://doi.org/10.1088/1475-7516/2024/12/019How to cite it
Remo Garattini, Athanasios G. Tzikas (2024) Traversable wormholes induced by stress energy conservation: combining Casimir energy with a scalar field doi:10.1088/1475-7516/2024/12/019