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Noncommutative-Geometry Wormholes Based on the Casimir Ef.ect

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Journal of.High Energy Physics, Gravitation and Cosmology 2023年第1期9卷 295-300页

作者： peter k. f. kuhfittig Department of.Mathematics Milwaukee School of Engineering Milwaukee WI USA

While wormholes are as good a prediction of.Einstein’s theory as black.holes, they are subject to severe restrictions f.om quantum f.eld theory. In particular, holding a wormhole open requires a violation of.the null energy condition, calling f.r the existence of.exotic matter. The Casimir ef.ect has shown that this physical requirement can be met on a small scale, thereby solving a k.y conceptual problem. The Casimir ef.ect does not, however, guarantee that the small-scale violation is suf.icient f.r supporting a macroscopic wormhole. The purpose of.this paper is to connect the Casimir ef.ect to noncommutative geometry, which also aims to accommodate small-scale ef.ects, the dif.erence being that these can now be viewed as intrinsic properties of.spacetime. As a result, the noncommutative ef.ects can be implemented by modif.ing only the energy momentum tensor in the Einstein f.eld equations, while leaving the Einstein tensor unchanged. The wormhole can theref.re be macroscopic in spite of.the small Casimir ef.ect.

关键词： Traversable Wormholes Noncommutative Geometry Casimir Ef.ect

Periodic Signature Change in Spacetimes of.Embedding Class One

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International Journal of.Astronomy and Astrophysics 2022年第2期12卷 167-176页

作者： peter k. f. kuhfittig Department of.Mathematics Milwaukee School of Engineering Milwaukee Wisconsin USA

The idea of.an oscillating Universe has remained a topic of.interest even af.er the discovery of.dark.energy. This paper conf.rms this idea by means of.another well-established theory in general relativity, the embedding of.curved spacetimes in higher-dimensional f.at spacetimes: an n-dimensional Riemannian space is said to be of.embedding class m if.m +n is the lowest dimension of.the f.at space in which the given space can be embedded;here . So a f.ur-dimensional Riemannian space is of.class two and can theref.re be embedded in a six-dimensional f.at space. A line element of.class two can be reduced to a line element of.class one by a suitable coordinate transf.rmation. The extra dimension can be either spacelik. or timelik., leading to accelerating and decelerating expansions, respectively. Accordingly, it is proposed in this paper that the f.ee parameter occurring in the transf.rmation be a periodic f.nction 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 f.r an oscillating Universe and complements various models proposed in the literature.

关键词： Signature Change Oscillating Universe Embedding Class One

Noncommutative Geometry and MOND

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Journal of.High Energy Physics, Gravitation and Cosmology 2022年第3期8卷 642-646页

作者： peter k. f. kuhfittig Department of.Mathematics Milwaukee School of Engineering Milwaukee USA

Modif.ed Newtonian dynamics (MOND) is a hypothesized modif.cation of.Newton’s law of.universal gravitation to account f.r the f.at rotation curves in the outer regions of.galaxies, thereby eliminating the need f.r dark.matter. Although a highly successf.l 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 of.shoot of.string theory, can account f.r the f.at rotation curves and thereby provide an explanation f.r MOND. This paper extends an earlier heuristic argument by the author.

关键词： Noncommutative Geometry MOND f.at Galactic Rotation Curves Dark.Matter

Traversable Wormholes and the Brouwer f.xed-Point Theorem

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Journal of.Applied Mathematics and Physics 2020年第7期8卷 1263-1268页

作者： peter k. f. kuhfittig Department of.Mathematics Milwaukee School of Engineering Milwaukee WI USA

The Brouwer f.xed-point theorem in topology states that f.r any continuous mapping f.on a compact convex set into itself.admits a f.xed point, i.e., a point x0 such that f.x0) = x0. Under suitable conditions, this f.x... 详细信息

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

关键词： Traversable Wormholes Brouwer f.xed-Point Theorem

The Ef.ect of.Conf.rmal Symmetry on Charged Wormholes

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Journal of.Applied Mathematics and Physics 2016年第12期4卷 2117-2125页

作者： peter k. f. kuhfittig Department of.Mathematics Milwaukee School of Engineering Milwaukee WI USA

This paper discusses the ef.ect that conf.rmal symmetry can have on a charged wormhole. The analysis yields a physical interpretation of.the conf.rmal f.ctor in terms of.the electric charge. The rate of.change of.the conf.rmal f.ctor determines much of.the outcome, which ranges f.om having no solution to wormholes having either one or two throats.

关键词： Charged Wormholes Conf.rmal Symmetry

Accounting f.r Some Aspects of.Dark.Matter and Dark.Energy via Noncommutative Geometry

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Journal of.Modern Physics 2017年第3期8卷 323-329页

作者： peter k. f. kuhfittig Department of.Mathematics Milwaukee School of Engineering Milwaukee WI USA

The purpose of.this paper is to seek.a connection between noncommutative geometry, an of.shoot of.string theory, and certain aspects of.dark.matter and dark.energy. The f.rmer case is based on a simple mathematical argument showing that the main manif.station of.dark.matter in connection with f.at galactic rotation curves is also a consequence of.noncommutative geometry. The latter case requires an examination of.the local ef.ect of.noncommutative geometry and the subsequent extension to the global phenomenon of.an accelerating Universe.

关键词： Noncommutative Geometry Dark Matter Dark Energy

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

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Journal of.Applied Mathematics and Physics 2017年第4期5卷 933-938页

作者： peter k. f. kuhfittig Department of.Mathematics Milwaukee School of Engineering Milwaukee Wisconsin USA

The starting point in this note is f.R) modif.ed gravity in a cosmological setting. We assume a spatially f.at universe to describe late-time cosmology and the perf.ct-f.uid equation of.state to model the hypothesized dark.energy. Given that on a cosmological scale, f.R) modif.ed 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 f.r the accelerated expansion, or that (2) the equation of.state f.r dark.energy was f.r more complicated than the perf.ct-f.uid model and might even exclude a constant w.

关键词： Cosmological Constant f.R) Gravity

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

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Journal of.Modern Physics 2013年第1期4卷 30-34页

作者： peter k. f. kuhfittig Department of.Mathematics Milwaukee School of Engineering Milwaukee USA

It is shown in the f.rst 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 f.rces, the wormhole is suitable f.r a humanoid traveler. The second part of.the paper shows that the electric f.eld can be eliminated (Einstein gravity), but only by tolerating enormous tidal f.rces. Such a wormhole would still be capable of.transmitting signals.

关键词： Wormholes Quintessential Matter Einstein-Maxwell Gravity

Revisiting Galactic Rotation Curves Given a Noncommutative-Geometry Back.round

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Journal of.Modern Physics 2014年第17期5卷 1931-1937页

作者： peter k. f. kuhfittig Vance D. Gladney Department of.Mathematics Milwaukee School of Engineering Milwaukee USA

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

关键词： Galactic Rotation Curves Noncommutative Geometry