Anisotropic charged Heintzmann solution using gravitational decoupling through extended geometric deformation approach

Abstract

In this article, we consider a well-known charged isotropic Heintzmann solution and extend it to its anisotropic domain by using gravitational decoupling through extended geometric deformation (EGD) approach. This approach converts a complex system of field equations which corresponds to the total energy momentum tensor (EMT) into two less-complicated subsystems employing linear transformation on both radial and temporal metric coefficients. The first one is related to the standard Einstein-Maxwell field equations (EFEs), while the other one is related to additional source. We study the matching conditions at the surface of the gravitational source between inner and outer spacetime geometries and evaluate the expressions for thermodynamical quantities ρ tot , and using mimic constraint and equation of state (EoS). In order to check the viability of the anisotropic version of the solution, we consider three different realistic stars, namely SAXJ1808.4 − 3658, SMCX − 4 and PSRJ1614 − 2230, and analyze the behavior of the model against different values of intensity parameter, i.e. γ = 0, 0.2 and 0.3. We also study the situation when electric charge is not present.