Accounting for Some Aspects of Dark Matter and Dark Energy via Noncommutative Geometry

The purpose of this paper is to seek a connection between noncommutative geometry, an offshoot of string theory, and certain aspects of dark matter and dark energy. The former case is based on a simple mathematical argument showing that the main manifestation of dark matter in connection with flat galactic rotation curves is also a consequence of noncommutative geometry. The latter case requires an examination of the local effect of noncommutative geometry and the subsequent extension to the global phenomenon of an accelerating Universe.

Thin-Shell Wormholes Admitting Conformal Motions in Spacetimes of Embedding Class One

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 σis positive, while the surface pressure is negative, resulting in , 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.

Noncommutative-Geometry Wormholes Based on the Casimir Effect

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.

The Effect of Conformal Symmetry on Charged Wormholes

This paper discusses the effect that conformal symmetry can have on a charged wormhole. The analysis yields a physical interpretation of the conformal factor in terms of the electric charge. The rate of change of the conformal factor determines much of the outcome, which ranges from having no solution to wormholes having either one or two throats.

Noncommutative-Geometry Inspired Charged Wormholes with Low Tidal Forces

When Morris and Thorne first proposed that wormholes might be actual physical structures suitable for interstellar travel, they needed to pay close attention to certain traversability conditions such as low tidal forces, which placed severe constraints on the wormhole geometry. Even more problematical was the need for “exotic matter” resulting from the unavoidable violation of the null energy condition required to hold a wormhole open. The purpose of this paper is to overcome these problems by starting with the charged wormhole model of Kim and Lee and assuming a noncommutative-geometry background: the violation of the null energy condition can be attributed to the latter, while the electric charge allows the reduction of the tidal forces to acceptable levels without invoking the trivial zero-tidal-force assumption.

A Note on the Cosmological Constant in <i>f</i>(<i>R</i>) Gravity

The starting point in this note is f(R) modified gravity in a cosmological setting. We assume a spatially flat universe to describe late-time cosmology and the perfect-fluid equation of state to model the hypothesized dark energy. Given that on a cosmological scale, f(R) modified gravity must remain close to Einstein gravity to be consistent with observation, it was concluded that either (1) Einstein’s cosmological constant was the only acceptable model for the accelerated expansion, or that (2) the equation of state for dark energy was far more complicated than the perfect-fluid model and might even exclude a constant w.

Revisiting Galactic Rotation Curves Given a Noncommutative-Geometry Background

It was shown earlier by Rahaman et al. that a noncommutative-geometry background can account for galactic rotation curves without the need for dark matter. The smearing effect that characterizes noncommutative geometry is described by means of a Gaussian distribution intended to replace the Dirac delta function. The purpose of this paper is two-fold: 1) to account for the galactic rotation curves in a more transparent and intuitively more appealing way by replacing the Gaussian function by the simpler Lorentzian distribution proposed by Nozari and Mehdipour and 2) to show that the smearing effect is both a necessary and sufficient condition for meeting the stability criterion.

Wormholes Supported by a Combination of Normal and Quintessential Matter in Einstein and Einstein-Maxwell Gravity

It is shown in the first part of this paper that a combined model comprising ordinary and quintessential matter can support a traversable wormhole in Einstein-Maxwell gravity. Since the solution allows zero tidal forces, the wormhole is suitable for a humanoid traveler. The second part of the paper shows that the electric field can be eliminated (Einstein gravity), but only by tolerating enormous tidal forces. Such a wormhole would still be capable of transmitting signals.

Traversable Wormholes and the Brouwer Fixed-Point Theorem

The Brouwer fixed-point theorem in topology states that for any continuous mapping f on a compact convex set into itself admits a fixed point, i.e., a point x0 such that f(x0) = x0. Under suitable conditions, this fixed point corresponds to the throat of a traversable wormhole, i.e., b(r0) = r0 for the shape function b = b(r). The possible existence of wormholes can therefore be deduced from purely mathematical considerations without going beyond the existing physical requirements.

Exploration of Traversable Wormholes Sustained by an Extra Spatial Dimension

The main goal of this paper is to determine the effect of an extra dimension on a traversable wormhole. Here an earlier study by the author [Phys. Rev. D 98, 064041 (2018)] is extended in several significant ways. To begin with, the extra spatial dimension is assumed to be time dependent, while the redshift and shape functions, as well as the extra dimension, are functions of both r and l, the respective radial and extra coordinates;the last of these is therefore a function of r, l, and t. The main objective is to determine the conditions that allow the throat of the wormhole to be threaded with ordinary matter (by respecting the null energy condition) and that the same conditions lead to a violation of the null energy condition in the fifth dimension, which is therefore responsible for sustaining the wormhole. The dependence of the extra dimension on l and t is subject to additional conditions that are subsequently analyzed in this paper. Finally, the extra dimension may be extremely small or even curled up.

Periodic Signature Change in Spacetimes of Embedding Class One

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 of the flat space in which the given space can be embedded;here . So a four-dimensional Riemannian space is of class two and can therefore 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.

Macroscopic Traversable Wormholes: Minimum Requirements

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 1) introducing the additional conditions needed to ensure that the radial tidal forces can indeed be sufficiently low and 2) by viewing traversable wormholes as emergent phenomena, thereby increasing the likelihood of their existence.

Noncommutative Geometry and MOND

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 an explanation for MOND. This paper extends an earlier heuristic argument by the author.