Physical attributes of polytropic structures in theory of gravity

Tayyaba Naz; Adnan Malik; Tooba Zia; Saira Waheed; Ali H. Alkhalidi

doi:10.1140/epjc/s10052-025-14123-y

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 409
https://doi.org/10.1140/epjc/s10052-025-14123-y

Regular Article - Theoretical Physics

Physical attributes of polytropic structures in $F (R)$ $\mathbb {F}(R)$ theory of gravity

Tayyaba Naz¹, Adnan Malik²^,3^a, Tooba Zia¹, Saira Waheed⁴ and Ali H. Alkhalidi⁵

¹ National University of Computer and Emerging Sciences, Lahore Campus, Lahore, Pakistan
² School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang, China
³ Department of Mathematics, University of Management and Technology, Sialkot Campus, Lahore, Pakistan
⁴ Prince Mohammad Bin Fahd University, Al Khobar, Kingdom of Saudi Arabia
⁵ Department of Mathematics, King Khalid University, Abha, Saudi Arabia

^a adnanmalik_chheena@yahoo.com, adnan.malik@skt.umt.edu.pk

Received: 26 February 2025
Accepted: 22 March 2025
Published online: 11 April 2025

Abstract

The aim of this work is to study the general formalism and applications of polytropic stars within the framework of a well-famed modified theory of gravity namely $F (R)$ $\mathbb {F}(R)$ theory. To accomplish this task, we assume the static spherically symmetric and Schwarzschild spacetimes, respectively, for defining the star’s interior and exterior geometries. By applying two polytropic equations of state, we derive physically well-behaved solutions to $F (R)$ $\mathbb {F}(R)$ field equations. Firstly, we develop the hydrostatic equilibrium and Lane–Emden equations for the isotropic fluid case within this framework of gravity. Next, we analyze the impact of isotropic pressure on stellar structures and graphically assess the physical behavior of isotropic polytropes using energy conditions and stability criteria. Additionally, the physical acceptability conditions are examined for the proposed solutions. The results indicate that this theory produces more viable and stable polytropes as compared to general relativity.

© The Author(s) 2025

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