Two diverse models of embedding class one

Kuhfittig, Peter K. F.

doi:10.1016/j.aop.2018.03.001

Cited by 38 publications

(22 citation statements)

References 28 publications

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“…Physically reasonable static stellar structures via embedding have been found by Maurya and Govender [8], Maurya et al [9,10], and Singh et al [11]. Kuhfittig [12] used embeddings to study charged wormholes and flat rotation curves in spiral galaxies. The case of traversable wormholes was considered in Ref.…”

Section: Introductionmentioning

confidence: 85%

Embedding with Vaidya geometry

Николаев

Maharaj

2020

Eur. Phys. J. C

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The Vaidya metric is important in describing the exterior spacetime of a radiating star and for describing astrophysical processes. In this paper we study embedding properties of the generalized Vaidya metric. We had obtained embedding conditions, for embedding into 5-dimensional Euclidean space, by two different methods and solved them in general. As a result we found the form of the mass function which generates a subclass of the generalized Vaidya metric. Our result is purely geometrical and may be applied to any theory of gravity. When we apply Einstein’s equations we find that the embedding generates an equation of state relating the null string density to the null string pressure. The energy conditions lead to particular metrics including the anti/de Sitter spacetimes.

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Section: Introductionmentioning

confidence: 85%

Embedding with Vaidya geometry

Николаев

Maharaj

2020

Eur. Phys. J. C

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“…Karmarkar [37] developed a mandatory condition for a static and spherically symmetric line element to be of class one. In recent years, different researchers have considered the KMc to discussed the configurations of spherically symmetric compact objects [38][39][40][41][42]. Kuhfittig [43] developed wormhole geometry using KMc and shown that the embedding theory may provide the basis for a complete wormhole solution.…”

Section: Literature Surveymentioning

confidence: 99%

Traversable wormhole solutions in f(R) gravity via Karmarkar condition

Shamir

Fayyaz

2020

Eur. Phys. J. C

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Motivated by recent proposals of possible wormhole shape functions, we construct a wormhole shape function by employing the Karmarkar condition for static traversable wormhole geometry. The proposed shape function generates wormhole geometry that connects two asymptotically flat regions of spacetime and satisfies the required conditions. Further, we discuss the embedding diagram in three-dimensional Euclidean space to present the wormhole configurations. The main feature of current study is to consider three well-known f(R) gravity models, namely exponential gravity model, Starobinsky gravity Model and Tsujikawa f(R) gravity model. Moreover, we investigate that our proposed shape function provides the wormhole solutions with less (or may be negligible) amount of exotic matter corresponding to the appropriate choice of f(R) gravity models and suitable values of free parameters. Interestingly, the solutions obtained for this shape function generate stable static spherically symmetric wormhole structure in the context of non-existence theorem in f(R) gravity. This may lead to a better analytical representation of wormhole solutions in other modified gravities for the suggested shape function.

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“…To produce the desired wormhole solution, we prefer the opposite signature in line element (2) in order to be consistent with line element (1):…”

Section: The Solutionmentioning

confidence: 99%

“…The approach in this paper differs significantly from that in Ref. [2], which discusses charged wormholes admitting a one-parameter group of conformal motions, together with a new model to explain the flat galactic rotation curves without the need for dark matter.…”

Section: Introductionmentioning

confidence: 99%

Spherically symmetric wormholes of embedding class one

Kuhfittig

2019

Pramana - J Phys

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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 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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Two diverse models of embedding class one

Cited by 38 publications

References 28 publications

Embedding with Vaidya geometry

Embedding with Vaidya geometry

Traversable wormhole solutions in f(R) gravity via Karmarkar condition

Spherically symmetric wormholes of embedding class one

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