Effects of expansion-free condition on adiabatic collapse in f(G,T) gravity

This study explores the impact of $f\left(\mathrm{G,T}\right)$ gravity, where $G$ is the Gauss Bonnet invariant and $T$ is the trace of the energy–momentum tensor, on the adiabatic anisotropic spherical gravitating source under the expansion-free condition. We coupled the relativistic matter with spherical symmetric structure by applying $f\left(\mathrm{G,T}\right)=\alpha G^n+\lambda T$ Gauss–Bonnet model with a linear trace. To derive the collapse equation, we used the perturbation method on the field equations and the contracted Bianchi identities. The dynamics of instability range is depicted in Newtonian ($N$) and post-Newtonian (pN) regimes. Furthermore, instead of using the adiabatic index, we establish the instability range by looking at the density profile and anisotropic pressure configuration. We investigate the analytic solutions that meets the expansion-free condition. Finally, we have successfully achieved the original results obtained by Herrera et al. (2012) in General Relativity by setting $\alpha =\lambda =0$ in proposed cosmological model.