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Peter K. F. Kuhfittig

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

At least 55 records · Page 3Linked to original sources
arXiv2020

Wormholes with a barotropic equation of state admitting a one-parameter group of conformal motions

The theoretical construction of a traversable wormhole proposed by Morris and Thorne maintains complete control over the geometry by assigning both the shape and redshift functions, thereby leaving open the determination of the stress-energy tensor. This paper examines the effect of introducing the linear barotropic equation of state $p_r=ωρ$ on the theoretical construction. If either the energy density or the closely related shape function is known, then the Einstein field equations do not ordinarily yield a finite redshift function. If, however, the wormhole admits a one-parameter group of conformal motions, then both the redshift and shape functions exist provided that $ω<-1$. In a cosmological setting, the equation of state $p=ωρ$, $ω<-1$, is associated with phantom dark energy, which is known to support traversable wormholes.

gr-qc↗
arXiv2020

Accounting for the large radial tension in Morris-Thorne wormholes

It is well known that a Morris-Thorne wormhole can only be held open by violating the null energy condition, physically realizable by the use of "exotic matter." Unfortunately, even a small or moderately-sized wormhole would have a radial tension equal to that of the interior of a massive neutron star. So outside a neutron-star setting, such an outcome is problematical at best, calling for more than an appeal to exotic matter whose introduction had a completely different objective and with possibly different outcomes. The purpose of this paper is to account for the enormous radial tension in three ways: (1) directly invoking noncommutative geometry, an offshoot of string theory, (2) appealing to noncommutative geometry in conjunction with $f(R)$ modified gravity, and (3) determining the possible effect of a small extra dimension.

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arXiv2019

Seeking connections between wormholes, gravastars, and black holes via noncommutative geometry

Noncommutative geometry, an offshoot of string theory, replaces point-like objects by smeared objects. The resulting uncertainty may cause a black hole to be observationally indistinguishable from a traversable wormhole, while the latter, in turn, may become observationally indistinguishable from a gravastar. The same noncommutative-geometry background allows the theoretical construction of thin-shell wormholes from gravastars and may even serve as a model for dark energy.

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arXiv2019

Thin-shell wormholes from Kiselev black holes

This paper discusses the theoretical construction of thin-shell wormholes from Kiselev black holes. We assume a barotropic equation of state for the exotic matter on the shell. While most of these wormholes are unstable to linearized radial perturbations, a limit argument is used to show that under certain conditions, stable solutions can be found.

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arXiv2019

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 rotation curves in galaxies and clusters of galaxies 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.

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arXiv2019

Spherically symmetric wormholes of embedding class one

This paper generalizes an earlier result by the author based on well-established embedding theorems that connect the classical theory of relativity to higher-dimensional spacetimes. In particular, 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. To study traversable wormholes, we concentrate on spacetimes that can be reduced to embedding class one by a suitable transformation. It is subsequently shown that the extra degrees of freedom from the embedding theory provide the basis for a complete wormhole solution in the sense of obtaining both the redshift and shape functions.

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arXiv2019

Macroscopic traversable wormholes with zero tidal forces inspired by noncommutative geometry

This paper addresses the following issues: (1) the possible existence of macroscopic traversable wormholes, given a noncommutative-geometry background, and (2) the possibility of allowing zero tidal forces, given a known density. It is shown that whenever the energy density describes a classical wormhole, the resulting solution is incompatible with quantum field theory. If the energy density originates from noncommutative geometry, then zero tidal forces are allowed. Also attributable to the noncommutative geometry is the violation of the null energy condition. The wormhole geometry satisfies the usual requirements, including asymptotic flatness.

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arXiv2018

Two diverse models of embedding class one

Embedding theorems have continued to be a topic of interest in the general theory of relativity since these help connect the classical theory to higher-dimensional manifolds. This paper deals with spacetimes of embedding class one, i.e., spacetimes that can be embedded in a five-dimensional flat spacetime. These ideas are applied to two diverse models, a complete solution for a charged wormhole admitting a one-parameter group of conformal motions and a new model to explain the flat rotation curves in spiral galaxies without the need for dark matter.

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arXiv2018

Thin-shell wormholes from compact stellar objects

This paper introduces a new type of thin-shell wormhole constructed from a special class of compact stellar objects rather than black holes. The construction and concomitant investigation of the stability to linearized radial perturbations commences with an extended version of a regular Hayward black hole. Given the equation of state $\mathcal{P}=ωσ$, $ω<0$, for the exotic matter on the thin shell, it is shown that whenever the value of the Hayward parameter is below its critical value, no stable solutions can exist. If the Hayward parameter is allowed to exceed its critical value, stable solutions can be found for moderately sized thin shells. Not only are the underlying structures ordinary compact objects, rather than black holes, the results are consistent with the properties of neutron stars, as well as other compact stellar objects.

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arXiv2017

Conformal-symmetry wormholes supported by a perfect fluid

This paper presents a new wormhole solution by assuming that a homogeneously distributed fluid with equation of state $p=ωρ$ can be adapted to an anisotropic spacetime such as a wormhole and that this spacetime admits a one-parameter group of conformal motions. The pressure $p$ in the equation of state becomes the lateral pressure $p_t$ instead of the radial pressure $p_r$, as assumed in previous studies. Given that $p_t=ωρ$, $p_r$ is then determined from the Einstein field equations. A wormhole solution can be obtained only if $ω<-1$ or $0<ω<1$. Since the former case corresponds to phantom dark energy, which has been the subject of earlier studies, we concentrate mainly on the latter. This case implies that given the above conditions, dark matter can support traversable wormholes.

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arXiv2017

A note on the cosmological constant in f(R) 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 $p=ωρ$ 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 is the only acceptable model for the accelerated expansion or (2) that the equation of state for dark energy is far more complicated than the perfect-fluid model and may even exclude a constant $ω$.

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arXiv2017

A note on wormholes in slightly modified gravitational theories

Wormholes that meet the flare-out condition violate the weak energy condition in classical general relativity. The purpose of this note is to show that even a slight modification of the gravitational theory could, under certain conditions, avoid this violation for matter threading the wormhole. The first part discusses some general criteria based on the field equations, while the second part assumes a specific equation of state describing normal matter, together with a particular type of shape function. The analysis is confined to wormholes with zero tidal forces.

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arXiv2016

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.

gr-qc↗
arXiv2016

Stable phantom-energy wormholes admitting conformal motions

It has been argued that wormholes are as good a prediction of Einstein's theory as black holes but the theoretical construction requires a reverse strategy, specifying the desired geometric properties of the wormhole and leaving open the determination of the stress-energy tensor. We begin by confirming an earlier result by the author showing that a complete wormhole solution can be obtained by adopting the equation of state $p=ωρ$ and assuming that the wormhole admits a one-parameter group of conformal motions. The main purpose of this paper is to use the assumption of conformal symmetry to show that the wormhole is stable to linearized radial perturbations whenever $-1.5<ω<-1$.

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arXiv2016

Gravitational lensing of wormholes in noncommutative geometry

It has been shown that a noncommutative-geometry background may be able to support traversable wormholes. This paper discusses the possible detection of such wormholes in the outer regions of galactic halos by means of gravitational lensing. The procedure allows a comparison to other models such as the Navarro-Frenk-White model and f(R) modified gravity and is likely to favor a model based on noncommutative geometry.

gr-qc↗
arXiv2016

Exactly solvable wormhole and cosmological models with a barotropic equation of state

An exact solution of the Einstein field equations given the barotropic equation of state $p=ωρ$ yields two possible models: (1) if $ω<-1$, we obtain the most general possible anisotropic model for wormholes supported by phantom energy and (2) if $ω>0$, we obtain a model for galactic rotation curves. Here the equation of state represents a perfect fluid which may include dark matter. These results illustrate the power and usefulness of exact solutions.

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arXiv2016

A note on the predictability of flat galactic rotation curves

Based on an exact solution of the Einstein field equations, it is proposed in this note that the dark-matter hypothesis could have led to the prediction of flat galactic rotation curves long before the discovery thereof by assuming that on large scales the matter in the Universe, including dark matter, is a perfect fluid.

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