Complexity‐Free Anisotropic Solution of Buchdahl's Model and Energy Exchange Between Relativistic Fluids by Extended Gravitational Decoupling

Abstract

AbstractIn this work, we present an anisotropic generalization of the Buchdahl static stellar model by implementing the method of extended gravitational decoupling and further requirement of vanishing complexity (Herrera, Phys Rev D 97:044010,2018). Starting off with a general spherically symmetric static metric with two unknown gravitational potentials, we impose the condition of vanishing complexity which then reduces the problem to a single‐generating metric function [Contreras and Stuchlik, Eur. Phys. J. C (2022) 82:706]. The Buchdahl ansatz is then employed to obtain the complete gravitational behavior of the isotropic seed solution. The method of extended gravitational decoupling is thereafter utilized to obtain an anisotropic counterpart of the Buchdahl perfect gravitating sphere. We subject our solution to rigorous physical tests to ensure that it serves as a viable candidate for compact objects such as neutron stars as well as pulsars. We show that the decoupling parameter plays a crucial role in determining the stability and regularity of several key physical features of the entire stellar model. A novel finding of our investigation is the energy exchange between the seed solution and the secondary source which we show is sensitive to the decoupling parameter. In addition, it has also been shown that the direction of energy flow depends on the radial distance of the shell from the center of the stellar configuration.