Scenarios of cosmic string with variable cosmological constant

Abstract

Exact solutions of the Einstein field equations with cosmic string and space varying cosmological constant, viz., $Λ= Λ(r)$, in the energy-momentum tensors are presented. Three cases have been studied: where variable cosmological constant (1) has power law dependence, (2) is proportional to the string fluid density, and (3) is purely a constant. Some cases of interesting physical consequences have been found out such that (i) variable cosmological constant can be represented by a power law of the type $Λ=3r^{-2}$, (ii) variable cosmological constant and cosmic string density are interdependent to each other according to the relation $Λ=-8πρ_s$, and (iii) cosmic string density can be scaled by a power law of the type $ρ_s=r^{-2}$. It is also shown that several known solutions can be recovered from the general form of the solutions obtained here.