New models for perfect fluids in EGB gravity

Abstract

We obtain new exact solutions to the field equations in the Einstein–Gauss–Bonnet (EGB) modified theory of gravity for a five-dimensional spherically symmetric static matter distribution. By using a coordinate transformation, the study is reduced to the analysis of a single first-order nonlinear differential equation which is an Abel equation of the second kind. Three classes of exact models are generated. The first solution has a constant density and a nonlinear equation-of-state; it contains the familiar Einstein static universe as a special case. The second solution has variable energy density and is expressible in terms of elementary functions. The third solution has vanishing Gauss–Bonnet coupling constant and is a five-dimensional generalization of the Durgapal–Bannerji model. The solution is briefly examined for physical admissibility. In particular, a set of constants is found which ensures that a pressure-free hypersurface exists which in turn defines the boundary of the distribution. The matter distribution is well behaved and the adiabatic sound speed criterion is also satisfied within the fluid ensuring a subluminal sound speed. Furthermore, the weak, strong and dominant conditions hold throughout the distribution.