arXiv subjects

Peter K. F. Kuhfittig

Publications and source records attributed to Peter K. F. Kuhfittig.

At least 37 records · Page 2Linked to original sources

arXiv2023

More on traversable wormholes sustained by an extra spatial dimension

This paper extends an earlier study by the author [Phys. Rev. D, vol. 98, 064041 (2018), arXiv:1809.01993] 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 main goal 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 can therefore be credited with helping to sustain the wormhole. The dependence of the metric coefficients on $l$ and time $t$ may either help or hinder the ability to use ordinary matter, while an unrestricted dependence on the fifth dimension could lead to a curvature singularity at the throat. Finally, the extra dimension may be extremely small or even curled up.

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arXiv2023

Traversable wormholes sustained by an extra spatial dimension

This paper explores the effect of an extra spatial dimension on a Morris-Thorne wormhole. After proposing a suitable model, it is shown that under certain conditions, the throat of the wormhole can be threaded with ordinary matter, while the unavoidable violation of the null energy condition can be attributed to the existence of the extra dimension.

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arXiv2023

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.

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arXiv2023

Revisiting wormholes supported by two non-interacting fluids

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.

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arXiv2022

Accounting for exotic matter and the extreme radial tension in Morris-Thorne wormholes of embedding class one

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.

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arXiv2021

Neutron star interiors and topology change

Quark matter is believed to exist in the center of neutron stars. A combined model consisting of quark matter and ordinary matter is used to show that the extreme conditions existing in the center could result in a topology change, that is, in the formation of wormholes.

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arXiv2021

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 $x_0$ such that $f(x_0)=x_0$. Under certain conditions, this fixed point corresponds to the throat of a traversable wormhole, i.e., $b(r_0)=r_0$ 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.

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arXiv2021

Charged wormholes in spacetimes of embedding class one

The existence of charged black holes has suggested that wormholes may also be charged. The purpose of this paper is to construct a general model of a charged wormhole that proves to be a natural extension of the original Morris-Thorne wormhole. This goal is achieved by means of the classical embedding theory that has played a major role in the general theory of relativity.

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arXiv2021

Vacuum energy in a noncommutative-geometry setting

It has recently been proposed that vacuum energy is zero in spite of the quantum-field fluctuations that occur everywhere, even at absolute zero. The implication is that dark energy must have a different origin, unrelated to vacuum energy. It is proposed in this paper that noncommutative geometry, an offshoot of string theory, may provide such an origin due to its ability to account for the accelerated expansion.

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arXiv2021

A model for dark energy based on the theory of embedding

A long-standing topic of interest in the general theory of relativity is the embedding of curved spacetimes in higher-dimensional flat spacetimes. The main purpose this paper is to show that the embedding theory can account for the accelerated expansion of the Universe and thereby serve as a model for dark energy. This result is consistent with earlier findings based on noncommutative geometry. A secondary objective is to show that the embedding theory also implies that it is possible, at least in principle, for the accelerated expansion to reverse to become a deceleration.

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arXiv2021

On wormholes in spacetimes of embedding class one

An $n$-dimensional Riemannian space is said to be of embedding class $m$ if $n+m$ is the lowest dimension of the flat space in which the given space can be embedded. A spherically symmetric spacetime of class two can be reduced to class one by a suitable transformation of coordinates. Applied to wormholes, given a well-defined shape function $b=b(r)$, the resulting wormhole has an event horizon and is therefore nontraversable. On a macroscopic scale, $b(r)$ can be replaced by $m(r)$, the effective mass of a spherical star of radius $r$ with $m(0)=0$, to yield a valid solution. Spacetimes of embedding class one have been used successfully for modeling compact stellar objects. On a microscopic scale, one can invoke noncommutative geometry to obtain a charged nontraversable wormhole, i.e., an Einstein-Rosen bridge, and hence a model for a charged particle.

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arXiv2021

Slowly evolving noncommutative-geometry wormholes

This paper discusses noncommutative-geometry wormholes in the context of a cosmological model due to Sung-Won Kim. An ansatz suggested by the Friedmann-Lemaitre-Robertson-Walker (FLRW) model leads to the assumption that the matter content can be divided into two parts, a cosmological part depending only on time and a wormhole part depending only on space. These assumptions are sufficient for deriving a complete zero-tidal force wormhole solution. The wormhole is evolving due to the scale factor in the FLRW model; it is restricted, however, to the curvature parameters $k=0$ and $k=-1$. Unlike previous models, the noncommutative-geometry background affects both the wormhole part and the cosmological part of the solution.

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arXiv2021

On the nature of exotic matter in Morris-Thorne wormholes

It is well known that phantom energy, which is characterized by the equation of state $p=ωρ$, $ω<-1$, can support Morris-Thorne wormholes since it leads to a violation of the null energy condition. The purpose of this note is to show that the converse is also true in the following sense: for a typical shape function, the equation of state of exotic matter in the vicinity of the throat is given by $p_r=ωρ$, $ω<-1$, where $p_r$ is the radial pressure. Some implications thereof are also considered.

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arXiv2021

Noncommutative-geometry wormholes with isotropic pressure

The strategy adopted in the original Morris-Thorne wormhole was to retain complete control over the geometry at the expense of certain engineering considerations. The purpose of this paper is to obtain several complete wormhole solutions by assuming a noncommutative-geometry background with a concomitant isotropic-pressure condition. This condition allows us to consider a cosmological setting with a perfect-fluid equation of state. An extended form of the equation generalizes the first solution and subsequently leads to the generalized Chaplygin-gas model and hence to a third solution. The solutions obtained extend several previous results. This paper also reiterates the need for a noncommutative-geometry background to account for the enormous radial tension that is characteristic of Morris-Thorne wormholes.

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arXiv2021

Comparing $f(R)$ modified gravity and noncommutative geometry in the context of dark matter and traversable wormholes: a survey

Noncommutative geometry, as conceptualized by Nicolini, Smailagic, and Spallucci, may be viewed as a slight modification of Einstein's theory. The same can be said for $f(R)$ modified gravity for an appropriate choice of the function $f(R)$. Since such an $f(R)$ could be determined from the noncommutative-geometry background, these gravitational theories make very similar predictions in the discussion of (a) dark matter and (b) traversable wormholes; they can therefore be taken as equally viable models.

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arXiv2020

A note on the stability of Morris-Thorne wormholes

Two critical issues in the study of Morris-Thorne wormholes concerns the stability of such structures, as well as their compatibility with quantum field theory. This note discusses an important subset characterized by zero tidal forces. It is shown that such wormholes (1) are in stable equilibrium using a criterion based on the Tolman-Oppenheimer-Volkoff (TOV) equation and (2) are not in direct conflict with quantum field theory.

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arXiv2020

Noncommutative-geometry wormholes without exotic matter

A fundamental property of Morris-Thorne wormholes is the so-called flare-out condition that automatically results in a violation of the null energy condition (NEC) in classical general relativity. By contrast, in $f(R)$ modified gravity, the material threading the wormhole may actually satisfy the NEC, while, at the same time, the effective stress-energy tensor arising from the modified theory violates the NEC, thereby sustaining the wormhole. It is shown in this paper that noncommutative geometry, an offshoot of string theory, can be viewed as a special case of $f(R)$ gravity and can therefore sustain a wormhole without the use of exotic matter. It also provides a motivation for the choice of $f(R)$ in the modified gravitational theory.

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arXiv2020

Wormholes in f(R) gravity with a noncommutative-geometry background

This paper discusses the possible existence of traversable wormholes in f(R) modified gravity while assuming a noncommutative-geometry background, as well as zero tidal forces. The first part of the paper aims for an overview via several shape functions by determining the corresponding wormhole solutions and their properties. The solutions are made complete by deriving the modified-gravity functions F(r) and f(R), where F=df/dR. It is subsequently shown that the violation of the null energy condition can be attributed to the combined effects of f(R) gravity and noncommutative geometry. The second part of the paper reverses the strategy by starting with a special form of f(R) and determining the wormhole solution and the concomitant F(r). The approach in this paper differs in significant ways from that of Jamil et al.

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