Gravitational complexity factor of anisotropic polytropes in coincident gauge gravity

Abeer M. Albalahi; Akbar Ali; M. Z. Bhatti

doi:10.1140/epjc/s10052-025-14316-5

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 583
https://doi.org/10.1140/epjc/s10052-025-14316-5

Regular Article - Theoretical Physics

Gravitational complexity factor of anisotropic polytropes in coincident gauge $f (Q)$ $f(\mathbb {Q})$ gravity

Abeer M. Albalahi¹, Akbar Ali¹ and M. Z. Bhatti²^a

¹ Department of Mathematics, College of Science, University of Ha’il, Ha’il, Saudi Arabia
² Institute of Mathematics, University of the Punjab, 54590, Lahore, Pakistan

^a mzaeem.math@pu.edu.pk

Received: 12 April 2025
Accepted: 14 May 2025
Published online: 27 May 2025

Abstract

This work presents a novel characterization of complexity for gravitationally bound astrophysical configurations arising from two factors: (i) inhomogeneity and (ii) anisotropy in the complex arrangement of stellar structures. For this purpose, we employ the non-metricity-motivated gravitational model with a linear choice of coincident gauge $f (Q)$ $f(\mathbb {Q})$ gravity, given by $f (Q) = β_{0} Q + β_{1}$ $f(\mathbb {Q}) = \beta _0 \mathbb {Q} + \beta _1$ , where $β_{0}$ $\beta _0$ and $β_{1}$ $\beta _1$ are model parameters. Our analysis begins by postulating that a fluid distribution exhibiting density uniformity and pressure isotropy is characterized by a minimal (or zero) gravitational complexity factor. The novelty of this study lies in its ability to study the effect of non-metricity on the intricate mechanism of dense-matter static stars while also considering the effectiveness of the complexity factor in determining fluctuations in the Tolman mass for both complex and non-complex compact structures within a non-metricity framework. The variation in the Tolman gravitational mass is caused by a suggested formulation of anisotropic pressure and density non-uniformity. It is observed that in Einstein’s gravitational model, a stellar system that features both can exhibit zero complexity ( $Y_{TF} = 0$ $Y_{TF}=0$ ) if their contributions cancel out. On the other hand, the linear $f (Q)$ $f(\mathbb {Q})$ model compels the gravitational configuration to maintain $Y_{TF} \neq 0$ $Y_{TF}\ne 0$ due to non-metricity contributions, even when the fluid exhibits density uniformity and pressure anisotropy. Furthermore, we discuss the construction of anisotropic self-gravitating polytropes by coupling the $Y_{TF} = 0$ $Y_{TF}=0$ condition with a polytropic EoS. This underscores the importance of the zero-complexity criterion in modeling astrophysical compact systems.

© The Author(s) 2025

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