# Charge Gravastars in $f(T)$ Modified Gravity

## TL;DR

This paper investigates charged gravastar models within $f(T)$ modified gravity, deriving solutions for different cases, analyzing the shell structure, and applying junction conditions to understand their physical properties.

## Contribution

It introduces a detailed analysis of charged gravastars in $f(T)$ gravity, highlighting the conditions for their formation and providing analytical solutions for their structure.

## Key findings

- Gravastar formation is possible only for $f_{TT}=0$ case.
- Analytical solutions for physical quantities in the shell region are derived.
- Proper length, entropy, and energy content are proportional to shell thickness.

## Abstract

In the present work, we have discussed the four dimensional spherically symmetric steller system in the framework of modified $f(T)$ gravity theory with electro-magnetic field. The field equations have been written for two cases, either $T'=0$ or $f_{TT}=0$. Next we have discussed the charged gravastar model which has three regions: interior region, shell region and exterior region. In the interior region, we have found the solutions of all physical quantities like density, pressure, electro-magnetic field and also the metric coefficients for both the cases. For $T'=0$, gravastar cannot form but it forms only for the case $f_{TT}=0$. In the exterior region, we have obtained the exterior solution for vacuum model. In the shell region, we have assumed that the interior and exterior regions join together at a place, so the intermediate region must be thin shell with the approximation $h\ll 1$. Under this approximation, we have found the analytical solutions. The proper length of the thin shell, entropy and energy content inside the thin shell have been found and they are directly proportional to the proper thickness of the shell $\epsilon$ under the approximation ($\epsilon\ll 1$). According to the Darmois-Israel formalism, we have studied the matching between the surfaces of interior and exterior regions of the gravastar. The energy density, pressure, equation of state parameter on the surface and mass of the thin shell have been obtained.