Viable decoupled solutions in energy–momentum squared gravity

Abstract

The aim of this study is to discuss viable anisotropic solutions of self-gravitating system through a minimal geometric deformation approach in the perspective of $f(R, T^{2})$ gravity. In this regard, we assume two sources (seed and additional) for the static sphere. The seed source is considered to be isotropic, while the additional source induces anisotropy. The field equations are decoupled into two sets by deforming the radial metric function. The metric potentials of the Krori–Barua solution are employed to obtain exact solution of the field equations while three different constraints are used to find the solutions corresponding to the anisotropic source. Junction conditions are utilised to determine the values of unknown constants at the hypersurface. Finally, we check the viability and stability of the obtained solutions using the star candidate PSR J1614-2230. We show that all the three solutions satisfy the viability conditions. It is found that solution I is stable using both Herrara’s cracking as well as squared sound speed approach while solutions II and III are stable using only Herrara’s cracking approach.