A class of solutions for Einstein field equations with spatially varying cosmological constant in spherically symmetric anisotropic source

TL;DR

This paper derives a new class of solutions to Einstein's field equations for spherically symmetric anisotropic fluids with a spatially varying cosmological constant, highlighting its physical significance in astrophysics and cosmology.

Contribution

It introduces a novel interior solution with a spatially variable cosmological constant for anisotropic spheres, expanding the understanding of such models in general relativity.

Findings

Pressure and cosmological parameter vanish at center and boundary

Maximum cosmological constant occurs inside the sphere

Variable Λ is physically significant in astrophysics and cosmology

Abstract

In this work a class of interior solution for Einstein field equations corresponding to a spherically symmetric anisotropic fluid sphere has been obtained under the assumption that the cosmological constant is spatially variable. The solution obtained has the characteristics that the pressure and the cosmological parameter vanish at the centre and at the boundary with a maximum value somewhere inside the body. It has been argued that a variable $ \Lambda $ is as much important physically in Astrophysics as in Cosmology.