Analysis of the isothermal property in isotropic 4 D Einstein-Maxwell-Gauss-Bonnet stellar distributions

The four-dimensional Einstein-Gauss-Bonnet theory of gravity developed by Glavan and Lin (Phys. Rev. Lett. 124, 081301, 2020) has been amply demonstrated to be applicable to spherically symmetric distributions, notwithstanding its other criticisms. This formulation allows us to study the effects of higher curvature geometry on the evolution of stars in the traditional 4-dimensional setting. In particular, our interest in this work is charged distributions. Despite the fact that the associated Einstein-Maxwell-Gauss-Bonnet field equations require two prescriptions to close the system, the task of locating exact solutions is nontrivial. We exploit a technique relating the electric field intensity to one of the gravitational potentials in order to reduce the order of the governing differential equation, and in this context we construct the isothermal fluid configuration exhibiting an inverse square law fall off of the energy density, and for a choice of integration constants also admits a similar behaviour in the pressure. In general, the higher curvature terms negate the isothermal behaviour when the spatial metric potential is constant, unlike the Einstein case. The model constructed is shown to have the necessary qualitative features of realistic distributions as depicted in graphical plots for suitably selected parameter spaces. Notably a surface of vanishing pressure is evident and the model is adiabatically stable and causal. Given the isothermal feature, a central singularity is present as expected. This suggests that our fluid model may be interpreted as a shell of charged fluid in 4D EMGB enveloping some other physically viable core.