Study of the charged super-Chandrasekhar limiting mass white dwarfs in the $f(R,\mathcal{T})$ gravity

The equilibrium configuration of white dwarfs composed of a charged perfect fluid are investigated in the context of the $f(R,\mathcal{T})$ gravity, for which $R$ and $\mathcal{T}$ stand for the Ricci scalar and the trace of the energy-momentum tensor, respectively. By considering the functional form $f(R, \mathcal{T})=R+2\chi \mathcal{T}$, where $\chi$ is the matter-geometry coupling constant, and for a Gaussian ansatz for the electric distribution, some physical properties of charged white dwarfs were derived, namely: mass, radius, charge, electric field, effective pressure and energy density; their dependence on the parameter $\chi$ was also derived. In particular, the $\chi$ value important for the equilibrium configurations of charged white dwarfs has the same scale of $10^{-4}$ of that for non-charged stars and the order of the charge was $10^{20}$C, which is scales with the value of one solar mass, i.e., $\sqrt{G}M_\odot\sim 10^{20}$C. We have also shown that charged white dwarf stars in the context of the $f(R,\mathcal{T})$ have surface electric fields generally below the Schwinger limit of $1.3\times 10^{18}$V/m. In particular, a striking feature of the coupling between the effects of charge and $f(R,\mathcal{T})$ gravity theory is that the modifications in the background gravity increase the stellar radius, which in turn diminishes the surface electric field, thus enhancing stellar stability of charged stars. Most importantly, our study reveals that the present $f(R,T)$ gravity model can suitably explain the super-Chandrasekhar limiting mass white dwarfs, which are supposed to be the reason behind the over-luminous SNeIa and remain mostly unexplained in the background of general relativity (GR).