Eur. Phys. J. C (2024) 84: 293
https://doi.org/10.1140/epjc/s10052-024-12652-6

Regular Article - Theoretical Physics

Electromagnetic field on the complexity of minimally deformed compact stars

¹ Department of Mathematics, College of Science, University of Ha’il, Ha’il, Kingdom of Saudi Arabia
² Department of Mathematics, University of the Punjab, Quaid-i-Azam Campus, 54590, Lahore, Pakistan

^b mzaeem.math@pu.edu.pk

Received: 14 February 2024
Accepted: 3 March 2024
Published online: 20 March 2024

Abstract

In the context of this endeavor, we establish a simple protocol for formulating interior stellar solutions that exhibit spherically symmetric configurations against the backdrop of relativistic gravitational decoupling through radial metric deformation (minimal geometric deformation scheme). In this pursuit, we make use of the vanishing complexity factor (${\tilde{Y}}_{\mathit{TF}}$) condition, based on Herrera’s (Phys Rev D 97, 044010, 2018) innovative concept regarding the complexity of static or slowly evolving spherical matter configurations. The idea of a complexity factor emerges as the outcome of the orthogonal splitting of the Riemann–Christoffel tensor, which yields different scalar functions, known as structure scalars. The protocol is demonstrated by employing the Buchdahl and Tolman relativistic stellar ansatzes as isotropic seeds. Both of these ansatzes exhibit similar physical features, with a minor variation in their magnitudes in the case of ${\tilde{Y}}_{\mathit{TF}}\ne 0$, where $0\le \alpha <1$, and $\alpha$ represents a coupling parameter. However, when ${\tilde{Y}}_{\mathit{TF}}=0$, the Buchdahl stellar ansatz exhibits a uniform density matter configuration, while the Tolman model features an increasing pressure profile. The obtained relativistic stellar models satisfy the basic viability constraints required for the physically realistic configurations.