In this current study, our main focus is on modeling the specific charged compact star SAX J 1808.4-3658 (M = 0.88 $$M_{\odot }$$M ⊙ , R = 8.9 km) within the framework of $$f(R,\,T)$$f ( R , T ) modified gravity theory using the metric potentials proposed by Tolman–Kuchowicz (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) and the interior spacetime is matched to the exterior Reissner–Nordström line element at the surface of the star. Tolman–Kuchowicz metric potentials provide a singularity-free solution which satisfies the stability criteria. Here we have used the simplified phenomenological MIT bag model equation of state (EoS) to solve the Einstein–Maxwell field equations where the density profile ( $$\rho $$ρ ) is related to the radial pressure ( $$p_{\mathrm{r}}$$p r ) as $$p_{\mathrm{r}}(r) = (\rho - 4B_{\mathrm{g}})/3$$p r ( r ) = ( ρ - 4 B g ) / 3 . Furthermore, to derive the values of the unknown constants $$a,\, b,\, B,\, C$$a , b , B , C and the bag constant $$B_{\mathrm{g}}$$B g , we match our interior spacetime to the exterior Reissner–Nordström line element at the surface of stellar system. In addition, to check the physical validity and stability of our suggested model we evaluate some important properties, such as effective energy density, effective pressures, radial and transverse sound velocities, relativistic adiabatic index, all energy conditions, compactness factor and surface redshift. It is depicted from our current study that all our derived results lie within the physically accepted regime which shows the viability of our present model in the context of $$f(R,\,T)$$f ( R , T ) modified gravity.

In this work, we discuss the configuration of a gravastar (gravitational vacuum stars) in the context of $$f(R, \,T )$$f ( R , T ) gravity by employing the Mazur–Mottola conjecture (Mazur and Mottola in Report No. LA-UR-01-5067, 2001; Mazur and Mottola, Proc Natl Acad Sci USA 101:9545, 2004). The gravastar is conceptually a substitute for a black hole theory as available in the literature and it has three regions with different equation of states. By assuming that the gravastar geometry admits a conformal Killing vector, the Einstein–Maxwell field equations have been solved in different regions of the gravastar by taking a specific equation of state as proposed by Mazur and Mottola. We match our interior spacetime to the exterior spherical region which is completely vacuum and described by the Reissner–Nordström geometry. For the particular choice of $$f(R,\,T)$$f ( R , T ) of $$f(R, \,T )=R+2\gamma T$$f ( R , T ) = R + 2 γ T , here we analyze various physical properties of the thin shell and also present our results graphically for these properties. The stability analysis of our present model is also studied by introducing a new parameter $$\eta $$η and we explore the stability regions. Our proposed gravastar model in the presence of charge might be treated as a successful stable alternative of the charged black hole in the context of this version of gravity.