Dynamics of compact objects in higher-order curvature gravity using Finch–Skea spacetime

M. Ilyas; Nehad Ali Shah; Fawad Khan; Rashid Habib

doi:10.1140/epjc/s10052-025-14000-8

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 253
https://doi.org/10.1140/epjc/s10052-025-14000-8

Regular Article - Theoretical Physics

Dynamics of compact objects in higher-order curvature gravity using Finch–Skea spacetime

M. Ilyas¹^a, Nehad Ali Shah²^b, Fawad Khan¹ and Rashid Habib¹

¹ Institute of Physics, Gomal University, 29220, Dera Ismail Khan, KP, Pakistan
² Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 11623, Riyadh, Saudi Arabia

^a ilyas_mia@yahoo.com
^b nashah@imamu.edu.sa

Received: 12 January 2025
Accepted: 22 February 2025
Published online: 10 March 2025

Abstract

This paper explores anisotropic spherical structures within metric $f (R)$ $$ f(R) $$ gravity, where $R$ $$ R $$ is the Ricci scalar, extending general relativity to include functions of $R$ $$ R $$ modified gravitational effects. We analyze compact stars using Finch–Skea solutions under the models; $f (R) = R + α R^{2}, f = R + α R^{2} (1 + γ R),$ $f(R) = R + \alpha R^2, f = R + \alpha R^2 (1 + \gamma R),$ and $f = R + α R (e^{- \frac{R}{γ}} - 1) .$ $f = R + \alpha R \left( e^{-\frac{R}{\gamma }} - 1 \right) .$ These models help us examine how gravity modifications affect the internal structure and behavior of neutrons and strange stars. We investigate material variables such as density, pressures, anisotropy, and forces (gravitational, hydrostatic, anisotropic) through graphical analysis. The physical viability of the stellar models is assessed by evaluating energy conditions (NEC, WEC, SEC, and DEC) and the equation of state (EoS) parameter. We also examine the role of anisotropy in stability and structure, comparing the results with general relativity to highlight the implications of $f (R)$ $$ f(R) $$ gravity on compact stars. This study aims to enhance the understanding of how modified gravity theories could impact the properties of compact astrophysical objects.

© The Author(s) 2025

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