Comparing mathematical modeling approaches for compact objects: vanishing complexity and embedding class one approaches in spherically symmetric systems with static background

Abstract

Abstract This study delves into the realm of solving Einstein’s field equations within the framework of general relativity. In this paper, we present an exact solution derived through the vanishing complexity approach and offer a comparative analysis with the established embedding class one approach. This exploration sheds light on the efficacy and validity of these methods in generating solutions for Einstein’s field equations. Our study involves a comprehensive exploration of several key parameters, encompassing thermodynamic factors, causality conditions, stability evaluations, as well as analyses of the mass function. Based on our findings, it can be suggested that the vanishing complexity approach could serve as a viable alternative method to the embedding class one approach for the derivation of exact solutions of Einstein’s field equations.