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Periodic Signature Change in Spacetimes of embedding class one

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 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.

关键词： Signature Change Oscillating Universe embedding class one

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Thin-Shell Wormholes Admitting Conformal Motions in Spacetimes of embedding class one

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International Journal of Astronomy and Astrophysics 2024年第3期14卷 162-171页

作者： Peter K. F. Kuhfittig Department of Mathematics Milwaukee School of Engineering Milwaukee USA

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.

关键词： Thin-Shell Wormholes Conformal Symmetry embedding class one Exotic Matter

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Relativistic models of anisotropic superdense star in the regime of Karmarkar's condition

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Communications in Theoretical Physics 2023年第2期75卷 168-179页

作者： Bikram Keshari Parida Shreya Majumder Shyam Das Koushik Chakraborty Farook Rahaman Department of Physics Pondicherry UniversityKalapetPuducherry 605014India Department of Physics North Bengal St.Xavier’s CollegeJalpaiguriWest Bengal735135India Department of Physics Malda CollegeMalda 732101West BengalIndia Department of Physics Government College of EducationBurdwanWest Bengal712103India Department of Mathematics Jadavpur UniversityKolkata 700032West BengalIndia

We obtained a new class of solutions for a relativistic anisotropic compact star by utilizing the Karmarkar embedding *** obtain the closed-form solution a suitable form of one of the gravitational potentials has been chosen to determine the other by analyzing the Karmarkar *** resulting solutions are found to be well-behaved and regular and could describe a compact stellar *** the current estimated values of the mass and radius of the pulsar 4U1820-30 as input parameters,all the physically relevant parameters are shown to be well-behaved to a very good degree of accuracy.

关键词： anisotropic compact star embedding class one Karmarkar’s condition

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