# Screened and Unscreened Solutions for Relativistic Star in de Rham-Gabadadze-Tolley (dRGT) Massive Gravity

## TL;DR

This paper investigates static, spherical star solutions in dRGT massive gravity, revealing the absence of the Vainshtein mechanism in the minimal model and exploring deviations from flat spacetime in non-minimal models.

## Contribution

It introduces a new algebraic equation for the reference metric's radial coordinate and analyzes solution branches, highlighting differences between minimal and non-minimal dRGT models.

## Key findings

- Vainshtein mechanism absent in minimal dRGT model
- Two solution branches: Schwarzschild connection and deviation from flat space
- Discussion on boundary conditions and mass-radius relations for stars

## Abstract

We study the static and spherical symmetric (SSS) configurations in the non-minimal model of the de Rham-Gabadadze-Tolley (dRGT) massive gravity with a flat reference metric. Considering the modified Tolman-Oppenheimer-Volkoff (TOV) equation, the Bianchi identity, and energy-momentum conservation, we find a new algebraic equation for the radial coordinate of the reference metric. We demonstrate that this equation suggests an absence of the Vainshtein mechanism in the minimal model of the dRGT massive gravity, while it has two branches of solutions where one connects with the Schwarzschild space-time and another implies the significant deviation from the asymptotically flat space-time in the non-minimal model. We also briefly discuss the boundary conditions for the relativistic stars in the dRGT massive gravity and a potential relation with the mass-radius relation of the stars.