Exact EGB models for spherical static perfect fluids

Abstract

We obtain a new exact solution to the field equations for a 5-dimensional spherically symmetric static distribution in the Einstein–Gauss–Bonnet modified theory of gravity. By using a transformation, the study is reduced to the analysis of a single second order nonlinear differential equation. In general the condition of pressure isotropy produces a first order differential equation which is an Abel equation of the second kind. An exact solution is found. The solution is examined for physical admissibility. In particular a set of constants is found which ensures that a pressure-free hypersurface exists which defines the boundary of the distribution. Additionally the isotropic pressure and the energy density are shown to be positive within the radius of the sphere. 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. On setting the Gauss–Bonnet coupling to zero, an exact solution for 5-dimensional perfect fluids in the standard Einstein theory is obtained. Plots of the dynamical quantities for the Gauss–Bonnet and the Einstein case reveal that the pressure is unaffected, while the energy density increases under the influence of the Gauss–Bonnet term.