Non-static spherically symmetric spacetimes and their conformal Ricci collineations

Abstract

For a perfect fluid matter, we present a study of conformal Ricci collineations (CRCs) of non-static spherically symmetric spacetimes. For non-degenerate Ricci tenor, a vector field generating CRCs is found subject to certain integrability conditions. These conditions are then solved in various cases by imposing certain restrictions on the Ricci tensor components. It is found that non-static spherically symmetric spacetimes admit 5, 6 or 15 CRCs. In the degenerate case, it is concluded that such spacetimes always admit infinite number of CRCs.

Conformal Symmetries of the Energy–Momentum Tensor of Spherically Symmetric Static Spacetimes

“…It is obvious that for this case, the choice of observers as a timelike four-vector field u a = e −ν/2 δ a 0 is not appropriate, since it gives ρ = 0 due to the condition T 0 = 0. Thus, we use the spacelike four-velocity u a = e −λ/2 δ a 1 of the observers for the metric (8), which implies that Equations ( 31) and (32) give…”

“…So, we need to choose a spacelike four-velocity such as u a = e −λ/2 δ a r . Using Equations ( 31) and (32), this choice gives rise to an anisotropic fluid without heat flux, as follows:…”

“…[30]. The CRCs with a non-constant φ have been studied for the Friedmann-Robertson-Walker spacetimes [19], the general static spherically symmetric spacetimes [31], the non-static spherically symmetric spacetimes [32] and Kantowski-Sachs spacetimes [33]. For pp-waves, the relationship between CRCs and CKVs has been studied in Ref.…”

Killing Vector Fields of Static Cylindrically Symmetric Spacetime—A Rif Tree Approach

“…In this context, various non-static spacetime geometries are discussed according to their KVFs. Of significant interest is an extensive work by Hussain et al on non-static spherically symmetric spacetimes and their conformal Ricci collineations in 2019 [13].…”