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While wormholes are just as good a prediction of Einstein's theory as black holes, they are subject to severe restrictions from quantum field theory. To allow for the possibility of interstellar travel, a macroscopic wormhole would need to maintain sufficiently low radial tidal forces. It is proposed in this paper that the assumption of zero tidal forces, i.e., the limiting case, is sufficient for overcoming the restrictions from quantum field theory. The feasibility of this approach is subsequently discussed by (a) introducing the additional conditions needed to ensure that the radial tidal forces can indeed be sufficiently low and (b) by viewing traversable wormholes as emergent phenomena, thereby increasing the likelihood of their existence., Comment: 14 pages, no figures

This paper discusses the feasibility of thin-shell wormholes in spacetimes of embedding class one admitting a one-parameter group of conformal motions. It is shown that the surface energy density $\sigma$ is positive, while the surface pressure $\mathcal{P}$ is negative, resulting in $\sigma +\mathcal{P}<0$, thereby signaling a violation of the null energy condition, a necessary condition for holding a wormhole open. For a Morris-Thorne wormhole, matter that violates the null energy condition is referred to as "exotic." For the thin-shell wormholes in this paper, however, the violation has a physical explanation since it is a direct consequence of the embedding theory in conjunction with the assumption of conformal symmetry. These properties avoid the need to hypothesize the existence of the highly problematical exotic matter., Comment: 10 pages, no figures

In physical science, the concept of \emph{emergence} is often used to describe phenomena that occur at macroscopic scales but not at microscopic scales. The latter is usually referred to as a \emph{fundamental property} and the former as an \emph{emergent property}. In this paper, noncommutative geometry, often viewed as an offshoot of string theory, is the primary fundamental theory that gives rise to macroscopic wormholes and their properties, thereby becoming an emergent phenomenon. As a consequence of these considerations, we will reexamine the boundary conditions that characterize a Morris-Thorne wormhole, resulting in a modification of the wormhole structure., Comment: 10 pages, no figures. arXiv admin note: text overlap with arXiv:2312.08392

Holding a Morris-Thorne wormhole open requires a violation of the null energy condition, calling for the need for so-called exotic matter near the throat. Many researchers consider exotic matter to be completely unphysical in classical general relativity. It has been shown, however, that the existence of an extra macroscopic dimension can resolve this issue: the throat could be lined with ordinary matter, while the extra dimension is then responsible for the unavoidable energy violation. The purpose of this paper is to show that the extra dimension can be microscopic, a result that is consistent with string theory., Comment: 7 pages, no figures

While wormholes may be just as good a prediction of Einstein's theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, a wormhole can only be held open by violating the null energy condition, calling for the existence of "exotic matter," a condition that many researchers consider completely unphysical, enough to rule out macroscopic traversable wormholes. An equally serious problem is the enormous radial tension at the throat of a typical Morris-Thorne wormhole unless the wormhole has an extremely large throat size. It has been proposed that noncommutative geometry, an offshoot of string theory, may be the proper tool for addressing these issues. The purpose of this paper is two-fold: (1) to refine previous arguments to make a stronger and more detailed case for this proposal and (2) to obtain a complete wormhole solution from the given conditions., Comment: 9 pages, no figures. arXiv admin note: substantial text overlap with arXiv:2312.05266

It has been claimed that wormholes are just as good a prediction of Einstein's theory as black holes, but they are subject to severe restrictions from quantum field theory. The purpose of this paper is to show that the claim can be substantiated in spite of these restrictions., Comment: 18 pages, no figures

Noncommutative geometry, an offshoot of string theory, replaces point-like particles by smeared objects. These local effects have led to wormhole solutions in a semiclassical setting, but it has also been claimed that the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The implication is that noncommutative-geometry wormholes could be macroscopic. This result can be readily explained by considering the noncommutative-geometry background to be a fundamental property and the macroscopic wormhole spacetime to be emergent, according to an earlier version of this paper. However, it is shown in the present version that such wormholes could not be sufficiently massive to exist on a macroscopic scale. A major objective in this paper is to invoke $f(Q)$ gravity to provide the extra degrees of freedom to overcome these obstacles., Comment: 10 pages, no figures

This paper extends several previous studies of wormholes supported by two non-interacting fluids beginning with a combined model of ordinary matter and phantom dark energy with an anisotropic matter distribution. After noting that such wormholes could only exist on very large scales, the two-fluid model is extended to neutron stars, previously treated only for the isotropic case. The model is completed by incorporating certain generic features proposed by the author in an earlier study., Comment: 8 pages, no figures

This paper discusses traversable wormholes in a dark-energy setting by starting with a model due to Sung-Won Kim. This model, based on the Friedmann-Lemaitre-Robertson-Walker model, is combined with a generalized Kaluza-Klein model. It is well known that phantom dark energy can in principle support traversable wormholes due to the violation of the null energy condition (NEC), a necessary condition for holding a wormhole open. Since the phantom divide constitutes a serious barrier, we retain the dark-energy assumption $a''(t)>0$ but stay below the phantom divide. To show that the violation of the NEC can only come from the fifth dimension requires a careful analysis of the scale factor $a(t)$. While needed in the overall model, certain 1-forms lack this scale factor since the extra dimension, often assumed to be compactified, would not be affected by the cosmological expansion. The result is a viable wormhole model of the Sung-Won Kim type. Our main conclusion involves Morris-Thorne wormholes: due to the Kaluza-Klein gravity, we obtain a complete wormhole solution without crossing the phantom divide., Comment: 11 pages, no figures

While wormholes are as good a prediction of Einstein's theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null energy condition, calling for the existence of exotic matter. The Casimir effect has shown that this physical requirement can be met on a small scale, thereby solving a key conceptual problem. The Casimir effect does not, however, guarantee that the small-scale violation is sufficient for supporting a macroscopic wormhole. The purpose of this paper is to connect the Casimir effect to noncommutative geometry, which also aims to accommodate small-scale effects, the difference being that these can now be viewed as intrinsic properties of spacetime. As a result, the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The wormhole can therefore be macroscopic in spite of the small Casimir effect., Comment: 6 pages, no figures

Modified Newtonian dynamics (MOND) is a hypothesized modification of Newton's law of universal gravitation to account for the flat rotation curves in the outer regions of galaxies, thereby eliminating the need for dark matter. Although a highly successful model, it is not a self-contained physical theory since it is based entirely on observations. It is proposed in this paper that noncommutative geometry, an offshoot of string theory, can account for the flat rotation curves and thereby provide a justification for MOND. This paper extends an earlier heuristic argument by the author., Comment: 5 pages, no figures

The idea of an oscillating Universe has remained a topic of interest even after the discovery of dark energy. This paper confirms this idea by means of another well-established theory in general relativity, the embedding of curved spacetimes in higher-dimensional flat spacetimes: an $n$-dimensional Riemannian space is said to be of embedding class $m$ if $m+n$ is the lowest dimension $d$ of the flat space in which the given space can be embedded; here $d=\frac{1}{2}n(n-1)$. So a four-dimensional Riemannian space is of class two since it can be embedded in a six-dimensional flat space. A line element of class two can be reduced to a line element of class one by a suitable coordinate transformation. The extra dimension can be either spacelike or timelike, leading to accelerating and decelerating expansions, respectively. Accordingly, it is proposed in this paper that the free parameter occurring in the transformation be a periodic function of time. The result is a mathematical model that can be interpreted as a periodic change in the signature of the embedding space. This signature change may be the best model for an oscillating Universe and complements various models proposed in the literature., Comment: 10 pages, no figures

A Morris-Thorne wormhole can only be sustained by violating the null energy condition, thereby requiring the existence of "exotic matter," a requirement that many researchers consider unphysical. Using a mostly qualitative approach, it is proposed in this note that the basic problems can be overcome by purely relativistic considerations. The implication is that a Morris-Thorne wormhole is likely to be a compact stellar object., Comment: 6 pages, no figures

It has been known for a long time that Morris-Thorne wormholes can only be held open by violating the null energy condition, which can be expressed in the form $\tau-\rho c^2>0$, where $\tau$ is the radial tension. Matter that violates this condition is usually referred to as "exotic." For any wormhole having a moderately-sized throat, the radial tension is equal to that at the center of a massive neutron star. Attributing this outcome to exotic matter seems reasonable enough, but it ignores the fact that exotic matter was introduced for a completely different reason. Moreover, its problematical nature suggests that the amount of exotic matter be held to a minimum, but this would make the high radial tension harder to explain. If the amount is infinitely small, this explanation breaks down entirely. By invoking $f(R)$ modified gravity, the need for exotic matter at the throat could actually be eliminated, but the negation of the above condition, i.e., $\tau <\rho c^2$, shows that we have not necessarily eliminated the high radial tension. This survey discusses various ways to account for the high radial tension and, in some cases, the possible origin of exotic matter. We conclude with some comments on a possible multiply-connected Universe., Comment: 14 pages, no figures

Embedding theorems, which have a long history in the general theory of relativity, are used in this paper to account for two of the most troubling aspects of Morris-Thorne wormholes, (1) the origin of exotic matter and the amount needed to sustain a wormhole, and (2) the enormous radial tension that is characteristic of wormholes with moderately-sized throats. Attributing the latter to exotic matter ignores the fact that exotic matter was introduced for a completely different reason and is usually present in only small quantities., Comment: 8 pages, no figures. arXiv admin note: text overlap with arXiv:2202.00051

The embedding of a curved spacetime in a higher-dimensional flat spacetime has continued to be a topic of interest in the general theory of relativity, as exemplified by the induced-matter theory. This paper deals with spacetimes of embedding class one, i.e., spacetimes that can be embedded in a five-dimensional flat spacetime. Einstein's theory allows the fifth dimension to be either spacelike or timelike. By assuming the latter, this paper addresses two fundamental issues concerning Morris-Thorne wormholes, the origin of exotic matter and the frequently inexplicable enormous radial tension at the throat., Comment: 8 pages, no figures