Stellar Structures in $f(\mathcal{G})$ Gravity Admitting Noether Symmetries

TL;DR

This paper explores the structure of compact stars within $f( ext{G})$ gravity using Noether symmetries, deriving solutions that align with observational data and reveal the influence of conserved quantities and model parameters.

Contribution

It introduces a novel application of Noether symmetry approach to $f( ext{G})$ gravity for modeling relativistic stellar objects, providing physically consistent solutions.

Findings

Solutions depend on conserved quantities and model parameters.

Compact star features are consistent with astrophysical observations.

Noether symmetries facilitate physically viable stellar models.

Abstract

This work aims to investigate some possible emergence of relativistic compact stellar objects in modified $f(\mathcal{G})$ gravity using Noether symmetry approach. For this purpose, we assume static spherically symmetric spacetime in the presence of isotropic matter distribution. We construct Noether symmetry generators along with associated conserved quantities by considering the standard choice of viable $f(\mathcal{G})$ gravity model i.e. $f(\mathcal{G})= \alpha\mathcal{G}^{n}$, where $\alpha$ is the model parameter. In particular, we use conservation relation acquired from the classical Noether approach by imposing some appropriate initial conditions to construct the metric potentials. The obtained conserved quantity play vital role in describing the stellar structure of compact stars. Moreover, by considering an appropriate numerical solution, some salient features of compact stellar structures like effective energy density, pressure, energy conditions, stability against equilibrium of the forces and speed of sound are discussed by assigning the suitable values of model parameter involved. Our study reveals that the compact objects in $f(\mathcal{G})$ gravity from Noether symmetry approach depend on the conserved quantity obtained and the model parameter $\alpha$. In nutshell, Noether symmetries are quite helpful to generate solutions that follow physically accepted phenomena. Moreover, we observed that these obtained solutions are consistent with the astrophysical observational data, which depicts the viability of our proposed Noether symmetry scheme.