Charged strange star model in Tolman–Kuchowicz spacetime in the background of 5D Einstein–Maxwell–Gauss–Bonnet gravity

In this article, we provide a new model of static charged anisotropic fluid sphere made of a charged perfect fluid in the context of 5D Einstein–Maxwell–Gauss–Bonnet (EMGB) gravity theory. To generate exact solutions of the EMGB field equations, we utilize the well-behaved Tolman–Kuchowicz (TK) ansatz together with a linear equation of state (EoS) of the form $$p_r=\beta \rho -\gamma $$, (where $$\beta $$ and $$\gamma $$ are constants). Here the exterior space-time is described by the EGB Schwarzschild metric. The Gauss–Bonnet Lagrangian term $$\mathcal {L}_{GB}$$ is coupled with the Einstein–Hilbert action through the coupling constant $$\alpha $$. When $$\alpha \rightarrow 0$$, we obtain the general relativity (GR) results. Here we present the solution for the compact star candidate EXO 1785-248 with mass$$=(1.3 \pm 0.2)M_{\odot }$$; radius $$= 10_{-1}^{+1}$$ km. respectively. We analyze the effect of this coupling constant $$\alpha $$ on the principal characteristics of our model, such as energy density, pressure components, anisotropy factor, sound speed etc. We compare these results with corresponding GR results. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified Tolman–Oppenheimer–Volkoff (TOV) equation and the dynamical stability through the critical value of the radial adiabatic index.The mass-radius relationship is also established to determine the compactness factor and surface redshift of our model. In this way, the stellar model obtained here is found to satisfy the elementary physical requirements necessary for a physically viable stellar object