Emerging hyperbolic spaces and some considerations in AdS cosmology

Pigazzini, Alexander; Pinčák, Richard; Jafari, Saeid; Özel, Cenap

doi:10.1142/s0219887822500621

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…(In fact, in this circumstance, if we consider a Kuranishi neighborhood (R d , E, s), with manifold R d , obstruction bundle E → R d , and section s : R d → E, then the dimension of the derived manifold F is dim(R d ) − rank(E), see [13]), and for rank(E) = 2d, the manifolds considered would coincide with the PNDP-manifolds (see [14], [15] and [16]). Therefore the existence of the solution shown above, for λ > 0, is also valid in the context of the PNDP-manifolds (in particular for PNDP-manifolds with positive virtual dimension), where its base-manifold is the product between two conformal manifolds to a n -dimensional and n-dimensional pseudo-Euclidean space, respectively.…”

Section: Conformal B-metricsmentioning

confidence: 99%

A family of special case of sequential warped product manifolds with semi-Riemannian Einstein metrics

Pigazzini¹,

Özel²,

Jafari³

et al. 2022

Preprint

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We derive the general formulas for a special configuration of the sequential warpedproduct semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a conformal metrics. Subsequently we study the case in which these two manifolds are conformal to a n -dimensional and n-dimensional pseudo-Euclidean space, respectively. For the latter case, we prove the existence of a family of solutions that are invariant under the action of a (n − 1)-dimensional group of transformations to the case of positive constant Ricci curvature (λ > 0).

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Section: Conformal B-metricsmentioning

confidence: 99%

A family of special case of sequential warped product manifolds with semi-Riemannian Einstein metrics

Pigazzini¹,

Özel²,

Jafari³

et al. 2022

Preprint

Self Cite

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show abstract

“…Even the Weyl tensor arises from dimensions. According to a valid definition of the term "virtual dimension", A. Pigazzini et al presented PNDP-manifolds, in [1,2,3,4,5,6,7], which have since shown to be extremely adaptable from an implementation perspective in a number of various research areas. For models of PNDP-manifolds, with positive, zero and negative "virtual dimensions" the authors of the works previously mentioned have shown the possibility of using these as well as their interpretation.…”

Section: Introductionmentioning

confidence: 99%

Emerging Electric or Magnetic Parts of Weyl Tensor on PNDP- Manifold

Sati¹,

Petwal

Pigazzini³

et al. 2023

Preprint

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In the present paper, we study the PNDP- manifold, which has shown to be effective in applications, particularly in the field of general relativity, by introducing a new topological approach to the emergent electric or magnetic parts associated to the Weyl tensor. The working hypothesis in this study is that the electric or magnetic parts of the Weyl tensor are the dimensions of the PNDP - manifold and the interaction that emerges as ”virtual” pointlike manifolds and as a manifold with positive/ negative dimensions results in the generation of the purely electric or purely magnetic parts of the Weyl tensor. The PNDP metric for the electric or magnetic parts of the Weyl tensor is also derived. The generalized Lorentz transformations on the PNDP manifold are introduced. These can give rise to novel forms of gauge theories if we consider local Lorentz transformations. Also we briefly show that principal fiber bundles with PNDP manifolds as base manifolds can be constructed. Mathematics Subject classifiction (2010): 53C25; 83C99; 53A45; 53B50

show abstract

Emerging electric or magnetic parts of Weyl tensor

Sati,

Petwal,

Pigazzini

et al. 2023

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

In this paper, we study the PNDP-manifold, which has shown to be effective in applications, particularly in the field of general relativity, by introducing a new topological approach to the emergent electric or magnetic parts associated to the Weyl tensor. The working hypothesis in this study is that the electric or magnetic parts of the Weyl tensor are the dimensions of the PNDP-manifold and the interaction that emerges as “virtual” point-like manifolds and as a manifold with positive/ negative dimensions results in the generation of the purely electric or purely magnetic parts of the Weyl tensor. The PNDP metric for the electric or magnetic parts of the Weyl tensor is also derived. The generalized Lorentz transformations on the PNDP manifold are introduced. These can give rise to novel forms of gauge theories if we consider local Lorentz transformations. Also we briefly show that principal fiber bundles with PNDP manifolds as base manifolds can be constructed.

show abstract

Emerging hyperbolic spaces and some considerations in AdS cosmology

Cited by 3 publications

References 10 publications

A family of special case of sequential warped product manifolds with semi-Riemannian Einstein metrics

A family of special case of sequential warped product manifolds with semi-Riemannian Einstein metrics

Emerging Electric or Magnetic Parts of Weyl Tensor on PNDP- Manifold

Emerging electric or magnetic parts of Weyl tensor

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