Theory of Traversable Wormholes without using Exotic Matter or Negative Energy in Einstein-Gauss-Bonnet-Dilaton (a String Gravity) theory

This is the second theory of Traversible Wormholes (dependent upon the actual physics of the universe) that we have covered recently.

This version is if string theory is true and universal inflation is true then traversable wormholes are possible without exotic matter or negative energy

Another solution for wormhole stargates depending on understanding the nature of electrons in terms of a semi-classical extension of the exact, general relativistic electron model of Arnowitt, Deser, and Misner (ADM), and Mach’s Principle could enable wormholes. The ADM model of the electron means that there is a lot of hidden negative mass and Mach’s principle could offer a means to shield or utilize the gravity of the universe. Mach effect would use bulk acceleration of capacitors to shield matter from universal gravity and thus expose the bare mass of the electrons. According to the ADM model the bare mass would be a very large negative amount which would provide the negative mass of Jupiter needed for some theoretical designs of Stargate wormhole.

Arxiv – Stable Lorentzian Wormholes in Dilatonic Einstein-Gauss-Bonnet Theory (29 pages)

We discuss the properties of Lorentzian wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions. These wormholes do not need any form of exotic matter for their existence. A subset of these wormholes is shown to be linearly stable with respect to radial perturbations. We perform a comprehensive study of their domain of existence, and derive a generalised Smarr relation for these wormholes. We also investigate their geodesics determining all possible particle trajectories, and perform a study of the acceleration and tidal forces that a traveler crossing the wormhole would feel.

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Wheeler suggested that quantum fluctuations would transform the gently undulating fabric of space-time at close range into a seething mass of complex shapes, known as quantum foam. According to this picture, exceedingly small wormholes with different topologies would appear and disappear in a flash.

Yet there is a natural process that could already have magnified these wormholes, making them large enough to travel through today. Inflation, as we call it, is widely thought to have operated in the first split-second of the universe’s existence, prompting it to balloon enormously and at breathtaking speed. “At the same time, it could have ballooned the tiny wormholes that make up the sub-microscopic fabric of space,” says Kleihaus.

For it to be traversable, the differences in gravity across a body travelling through the wormhole must be small enough to keep the body intact. The good news, says Kleihaus, is that the photons and subatomic particles can easily travel through. The bad news is that for a massive human being to travel through unscathed by gravity, the wormhole mouth needs to curve very gently and this means it must be tens to hundreds of light years across.

In general, though, even enormous wormholes will be difficult to spot. When hidden by dust and gas and stars, they look very similar to black holes. It is even possible that Sagittarius A*, the supermassive black hole at the centre of our Milky Way, could be a wormhole. One way to be sure, says Kleihaus, would be to study matter falling in.

While the wormhole solution found so far in DEGB theory connects our universe to another, it is still possible that other solutions exist that connect different parts of our universe. Kleihaus and his colleagues intend to investigate this possibility. Such a wormhole would open up the prospect of an extraterrestrial subway system.

Any advanced aliens using such a wormhole have to position the wormhole to prevent anything that is too large from passing into it, because that would collapse the wormhole.

In this work, we will investigate the properties of wormhole solutions that arise in the context of the fourdimensional dilatonic Einstein-Gauss-Bonnet theory, first reported in this paper- Possible wormholes in a brane world. The presence of the higher-curvature GB term, that follows naturally from the compactification of the 10-dimensional heterotic superstring theory down to four dimensions, suffices to support these types of solutions without the need for phantom scalar fields or other forms of exotic matter.

The outline of our paper is as follows: In section II, we present the theoretical context of our model and discuss the asymptotic forms of the sought-for wormhole solutions at the regions of radial infinity and the regular throat. Based on the latter, we derive the embedding diagram and study the violation of the energy conditions. We also present a Smarr relation for the wormhole solutions. In section III, we present the results of our numerical analysis that reveal the existence of wormhole solutions in the dilatonic Einstein-Gauss-Bonnet theory, and discuss their properties. We demonstrate the stability with respect to radial perturbations of a subset of these solutions in section IV. In section V we discuss the junction conditions. The geodesics in these wormhole spacetimes are presented in section VI. We calculate the magnitude of the acceleration and tidal forces that a traveler traversing the wormhole would feel in section VII, and conclude in section VIII.

The existence of traversable wormholes in the context of General Relativity relies on the presence of some form of exotic matter. However, in the framework of a string-inspired generalized theory of gravity, the situation may be completely different. Here we have investigated wormhole solutions in Einstein-Gauss-Bonnet-Dilaton (EGBd) theory, which corresponds to a simplified action that is motivated by the low-energy heterotic string theory. Indeed, as we have demonstrated, EGBd theory allows for stable, traversable wormhole solutions, without the need of introducing any form of exotic matter. The violation of the energy conditions, that is essential for the existence of the wormhole solutions, is realized via the presence of an effective energy-momentum tensor generated by the quadratic-in-curvature Gauss-Bonnet term.

We have determined the domain of existence of these wormhole solutions and shown that it is bounded by three sets of limiting solutions. The first boundary consists of the EGBd black hole solutions of [formula]. The second boundary is approached asymptotically, when the curvature radius at the throat of the wormhole diverges (the f0 → ∞ limit). Finally, at the third boundary, solutions with a curvature singularity at a finite distance from the throat are encountered.

We have investigated the properties of these EGBd wormholes and derived a Smarr-like mass relation for them. In this, the horizon properties in the black hole case are replaced by the corresponding throat properties of the wormholes, thus the area and surface gravity here refer to the ones at the throat. Moreover, as is well known for black holes in EGB theories, their entropy does not correspond merely to their horizon area but it receives a GB correction term. Similarly, we find that the mass formula for the wormhole solutions includes an analogous GB correction term; in addition, another term, that vanishes in the black hole case, appears that represents the GB corrected dilaton charge at the throat. We have demonstrated that the Smarr relation is satisfied very well by the numerical solutions.

We have also investigated the stability of the solutions. We have shown that a subset of our wormhole solutions, the one that lies close to the border with the linearly stable dilatonic black holes in the domain of existence, is also linearly stable with respect to radial perturbations. While we have also shown that another subset is unstable, we have concluded that the study of the standard equivalent Schr¨odinger equation cannot determine the stability for the full domain of existence We hope to resume the question of the existence of an alternative method for the study of the stability of all of our wormhole solutions at some future work.

When the wormhole solutions are extended to the second asymptotically flat region, this extension must be made in a symmetric way, since otherwise a singularity is encountered. As a consequence of this symmetric extension, the derivatives of the metric and dilaton functions become discontinuous at the throat. This discontinuity demands the introduction of some matter distribution at the throat. We have shown that this may be realized by the introduction of a perfect fluid at the throat whose energy density is positive for the subset of stable wormhole solutions.

Next, we have studied and classified the geodesics of massive and massless test particles in these wormhole spacetimes. Depending on the respective effective potential, there are two general kinds of trajectories for these particles. The particles may remain on bound or escape orbits within a single asymptotically flat part of the spacetime, or they may travel from one asymptotically flat part to the other on escape orbits, and travel back and forth on bound orbits.

In addition, we have calculated the acceleration and tidal forces which travelers traversing the wormhole would feel. We find that their magnitude may be small for fairly large values of the size of the throat of the wormhole. According to our findings, the radius of the wormhole throat is bounded from below only, therefore, the wormholes can be indeed arbitrarily large. Astrophysical consequences will be addressed in a forthcoming paper as well as the existence of stationary rotating wormhole solutions in the EGBd theory.

Other Research

The author of this paper has written many others on wormholes, blackholes, boson stars and monopoles.

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