# Study on anisotropic strange stars in $f(R,T)$ gravity: An embedding approach under simplest linear functional of matter-geometry coupling

## TL;DR

This paper investigates anisotropic strange stars within f(R,T) gravity using an embedding approach, deriving solutions with physical validity and predicting stellar radii that vary with the matter-geometry coupling parameter.

## Contribution

It introduces a novel anisotropic stellar model in f(R,T) gravity with a linear matter-geometry coupling, applying the embedding class one method and the MIT bag model for strange quark matter.

## Key findings

- Predicted radii decrease as the coupling parameter increases.
- Stars become more massive and dense with higher coupling values.
- Physical tests confirm the validity of the anisotropic solutions.

## Abstract

The present work is focused on the investigation of the existence of compact structures describing anisotropic matter distributions within the framework of modified gravity theories, specifically f(R,$\mathcal{T}$) gravity theory. Additionally, we have taken f(R,$\mathcal{T}$) as a linear function of the Ricci scalar $R$ and the trace of the energy-momentum tensor $\mathcal{T}$ as $f(R,\mathcal{T})$=$R+2\chi\mathcal{T}$,where $\chi$ is a dimensionless coupling parameter, and the Lagrangian matter $\mathcal{L}_m=-\frac{1}{3}\left(2p_{t}+p_{r}\right)$, to describe the complete set of field equations for the anisotropic matter distribution. We follow the embedding class one procedure using Eisland condition to obtain a full space-time description inside the stellar configuration. Once the space-time geometry is specified we determine the complete solution of the modified Einstein equations by using the MIT bag model equation of state $p_{r}=\frac{1}{3}\left(\rho-4B\right)$ that describes the strange quark matter (SQM) distribution inside the stellar system, where $B$ denotes a bag constant. The physical validity of our anisotropic solution is confirmed by executing several physical tests. It is worth mentioning that with the help of the observed mass values for the various strange star candidates we have predicted the exact radii by taking different values for $\chi$ and $B$. These predicted radii show monotonic decreasing nature as the parameter $\chi$ is moved from $-0.8$ to $0.8$ progressively. In this case, our anisotropic stellar system becomes more massive and transforms into more dense compact stars.