Spherically symmetric perfect fluid filled universe within the 4 dimensional Einstein–Gauss–Bonnet gravity formalism with vanishing conformal curvature

Abstract

Conformally flat spacetime geometry is of immense physical importance. In this context we obtain the most general solutions for 4 dimensional Einstein–Gauss–Bonnet (4D EGB) static spherically symmetric spacetimes. The standard Schwarzschild incompressible fluid sphere is one possible solution, however, new branches of solutions emerge that have cosmological significance. It is intriguing that the geometry of the new model is given by an exactly known spatially directed potential while the remaining potential is given as an integral. It is not necessary to know the explicit form of the temporally directed potential to analyze the physics of the model. However, at least two explicit exact solutions for both potentials are exhibited. Graphical plots are constructed to show that barring a short interval from the center of the distribution which may be excised and replaced with a well-behaved fluid, all the elementary physical tests are successful. The model considered does not admit a finite radius hence is not applicable to astrophysical compact objects however the pleasing physical characteristics of the fluid suggests applicability to a perfect fluid filled universe. The model satisfies the causality requirement preventing the sound speed from becoming superluminal as well as the Chandrasekar stability criterion demanded of adiabatic fluids. Moreover all the energy conditions are complied with. The analysis effectively rules out the existence of conformally flat stars in 4D EGB gravity aside from the interior Schwarzschild spacetime.