A space dependent Cosmological Constant

In a specific adiabatic perfect fluid, intrinsic entropy density perturbations are the source of a {\it space dependent} cosmological constant responsible for local void inhomogeneity. Assuming an anisotropic Locally Rotationally Symmetric space time, using the 1+1+2 covariant approach and a Lemaitre space time metric, we study the cosmological implication of such a scenario giving a proper solution to the Hubble constant tension and providing, locally, also an effective equation of state with $w\leq - 1$.