Work

Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times

Year: 2024

Type: article

Abstract: We establish two key results regarding pseudo symmetric and pseudo Ricci symmetric space-times. Firstly, we demonstrate that in pseudo symmetric generalized Robertson-Walker space-times either the scalar curvature remains constant or the associated vector field $$B_{i}$$ B i is irrotational. Secondly, in pseudo Ricci symmetric generalized Robertson-Walker space-times, we establish that either the scalar curvature is zero or the associated vector field $$A_{i}$$ A i is irrotational. We identify the conditions to ensure both $$B_{i}$$ B i and $$A_{i}$$ A i of these manifolds are acceleration-free and vorticity-free. We provide evidence that a pseudo symmetric and pseudo Ricci symmetric GRW space-time can be described as a perfect fluid. In a pseudo symmetric space-time, the state equation is given by $$p=\frac{4-n}{ 2n-2}\mu $$ p = 4 - n 2 n - 2 μ , whereas in a pseudo Ricci symmetric space-time, the state equation takes the form $$p=\frac{3-n}{n-1}\mu $$ p = 3 - n n - 1 μ , where p and $$\mu $$ μ are the isotropic pressure and the energy density. It is noteworthy that if $$n=4$$ n = 4 , a pseudo symmetric space-time corresponds to the dust matter era, while a pseudo Ricci symmetric space-time corresponds to the phantom era.

Source: Analysis and Mathematical Physics

DOI: 10.1007/s13324-024-00978-z

Authors: Abdallah Abdelhameed Syied, Uday Chand De, Nasser Bin Turki, Gabriel-Eduard Vîlcu

Institutions: Zagazig University, University of Calcutta, King Saud University, Romanian Academy, Universitatea Națională de Știință și Tehnologie Politehnica București

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: King Saud University