Modeling Compact Objects in $f(R)$ Gravity: Application of Buchdahl-I Metric with Chaplygin Equation of State

TL;DR

This paper models realistic anisotropic compact objects in $f(R)$ gravity using Buchdahl-I metric and Chaplygin equation of state, analyzing their physical properties and stability for specific pulsars.

Contribution

It introduces a novel application of Buchdahl-I metric with Chaplygin EoS in $f(R)$ gravity to model compact stars and assesses their physical viability and stability.

Findings

Physical parameters align with observational data

Models satisfy energy and causality conditions

Graphical analysis supports $f(R)$ gravity validity

Abstract

This paper investigates realistic anisotropic matter configurations for spherical symmetry in the framework of $f(R)$ gravity. The solutions obtained from Buchdahl-I metric are used to determine the behavior of PSR J0740+6620, PSR J0348+0432 and 4U 1608-52 with Starobinsky model. Analysis of physical parameters such as density, pressure, and anisotropy is illustrated through graphs, and the stability of compact objects is investigated by energy and causality conditions. We will also discuss the behavior of gravitational, hydrostatic and anisotropic forces, gravitational redshift and adiabatic index. At the theoretical and astrophysical scales, the graphical representations validate the practical and realistic $f(R)$ gravity models.