A note on classification of dust static plane symmetric space-times via proper curvature collineations in f(R) gravity

2022/03/24 by Aasma Nazir, Ghulam Shabbir, Fiaz Hussain +4
Physics and Astronomy · #Cosmology and Gravitation Theories #Advanced Differential Geometry Research #Black Holes and Theoretical Physics

paper · doi:10.1142/s0219887822500426

Abstract

In this paper, we classify dust static plane symmetric (SPS) space-times via proper curvature collineations (CCs) in the [Formula: see text] gravity using the rank of [Formula: see text] Riemann matrix and direct integration technique. Classifying the above mentioned space-times, we find that there arise six cases corresponding to specific values of the function [Formula: see text]. Inspecting all the cases, we reach at the fact that there exist two cases where the space-times admit proper CCs which form an infinite dimensional vector space (IDVS). In rest of the four cases, the space-time becomes either flat or CCs become the killing vector fields (KVFs).

Citations

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Classification of static spherically symmetric space-times in f(R) theory of gravity according to their conformal vector fields
• Dust static plane symmetric solutions and their conformal vector fields in <i>f</i>(<i>R</i>) theory of gravity
• A note on classification of spatially homogeneous rotating space-times in f(R) theory of gravity according to their proper conformal vector fields
• Classification of non-conformally flat static plane symmetric perfect fluid solutions via proper conformal vector fields in f(T) gravity

Related

• Dust static plane symmetric solutions and their conformal vector fields in <i>f</i>(<i>R</i>) theory of gravity
• Classification of static spherically symmetric space-times in f(R) theory of gravity according to their conformal vector fields
• A note on classification of spatially homogeneous rotating space-times in f(R) theory of gravity according to their proper conformal vector fields
• Classification of proper non-static cylindrically symmetric perfect fluid space-times via conformal vector fields in f(R) gravity
• Conformal vector fields in proper non-static plane symmetric spacetimes in f(R) gravity