Barotropic equations of state in 4D Einstein-Maxwell-Gauss-Bonnet stellar distributions

Abstract

We investigate the role of a linear barotropic equation of state ($p=\gamma \rho$) on the structure of charged stars under higher curvature effects induced by the Gauss-Bonnet invariants in 4 dimensions. Assuming a constant spatially directed potential which gives isothermal behavior in the standard theory, the master equation is solved in terms of hypergeometric functions but a viable model could not be constructed. Setting the temporal potential to a constant, comparable to the defective Einstein static universe, interestingly admits nontrivial nonconstant exact solutions due to the higher curvature terms unlike in general relativity. Next the existence of a one-parameter group of conformal motions in the spacetime geometry was investigated. The master differential equation is solvable exactly in implicit form and explicit solutions are found for special cases. For the case of a stiff fluid $p=\rho$ a stellar model with pleasing physical attributes is found. When the potential is assumed to vary linearly with the radius, an exact incoherent radiation model $p=\frac{1}{3}\rho$ emerges. The physical properties of both these solutions are analyzed comprehensively with the aid of graphical plots in conjunction with suitably defined parameter spaces. It was found that both exact models passed elementary astrophysical tests for physical plausibility.