A new anisotropic solution by MGD gravitational decoupling

Abstract

This paper is focused on the search for new anisotropic analytic solutions to Einstein’s field equations for a spherically symmetric and static stellar distribution by means of the gravitational decoupling realized via the Minimal Geometric Deformation (MGD) approach. Firstly, a Buchdahl perfect fluid inside the stellar distribution is considered and the Einstein’s field equations are used in order to obtain the explicit form of the pressure and density for the perfect fluid. Then, the matching conditions for stellar distributions are used to find the constants involved in the Buchdahl solution in order to ensure the geometric continuity at the stellar surface. Finally, the Buchdahl solution is deformed to obtain the anisotropic solution and the matching conditions are used to find the constants involved in the new solution. The result is a new analytic and well-behaved anisotropic solution, in which all their physical parameters, such as the effective density, the effective radial and tangential pressure, fullfill each of the requirements for the physical acceptability available in the literature. Therefore, this solution can give a satisfactory description of realistic astrophysical compact objects like stars.