Statistical conformal Killing Vector Fields for FLRW Space-Time

Fuente: arXiv
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Auteurs principaux: Peyghan, Esmaeil, Nourmohammadifar, Leila, Iosifidis, Damianos
Format: Preprint
Publié: 2024
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author Peyghan, Esmaeil
Nourmohammadifar, Leila
Iosifidis, Damianos
author_facet Peyghan, Esmaeil
Nourmohammadifar, Leila
Iosifidis, Damianos
contents The classification of conformal Killing vector fields for FLRW space-time from Riemannian point of view was done by Maartens-Maharaj in \cite{Maartens1986}. In this paper, we introduce conformal Killing vector fields from a new point of view for the FLRW space-time. In particular, we consider three cases for the conformal factor. Then, it is shown that there exist nine conformal vector fields on FLRW in total, such that six of them are Killing and the rest being non-Killing conformal vector fields. Consequently, by recalling the concept of statistical conformal Killing vector fields introduced in \cite{SP}, we classify statistical structures with repsect to which these vector fields are conformal Killing. We also obtain the form of affine connections that feature a vanishing Lie derivative with respect to these conformal Killing vector fields. Imposing the torsion-free and the Codazzi conditions on these connections, we study statistical structures on FLRW. Finally, for torsionful connections we study the vanishing of the Lie derivative of the torsion tensor with respect to these conformal Killing vector fields and derive the conditions under which this is valid.
format Preprint
id arxiv_https___arxiv_org_abs_2405_17165
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Statistical conformal Killing Vector Fields for FLRW Space-Time
Peyghan, Esmaeil
Nourmohammadifar, Leila
Iosifidis, Damianos
General Relativity and Quantum Cosmology
Mathematical Physics
Differential Geometry
The classification of conformal Killing vector fields for FLRW space-time from Riemannian point of view was done by Maartens-Maharaj in \cite{Maartens1986}. In this paper, we introduce conformal Killing vector fields from a new point of view for the FLRW space-time. In particular, we consider three cases for the conformal factor. Then, it is shown that there exist nine conformal vector fields on FLRW in total, such that six of them are Killing and the rest being non-Killing conformal vector fields. Consequently, by recalling the concept of statistical conformal Killing vector fields introduced in \cite{SP}, we classify statistical structures with repsect to which these vector fields are conformal Killing. We also obtain the form of affine connections that feature a vanishing Lie derivative with respect to these conformal Killing vector fields. Imposing the torsion-free and the Codazzi conditions on these connections, we study statistical structures on FLRW. Finally, for torsionful connections we study the vanishing of the Lie derivative of the torsion tensor with respect to these conformal Killing vector fields and derive the conditions under which this is valid.
title Statistical conformal Killing Vector Fields for FLRW Space-Time
topic General Relativity and Quantum Cosmology
Mathematical Physics
Differential Geometry
url https://arxiv.org/abs/2405.17165