Three dimensional Eddington-inspired Born-Infeld gravity: Solutions

Three dimensional Eddington-inspired Born-Infeld gravity is studied with the goal of finding new solutions. Beginning with cosmology, we obtain analytical and numerical solutions for the scale factor a(t), in spatially flat (k = 0) and spatially curved (k = +/-1) Friedmann-Roberston-Walker universes with (i) pressureless dust (P = 0) and (ii) perfect fluid (p = rho/2), as matter sources. When the theory parameter kappa > 0, our cosmological solutions are generically singular (except for the open universe, with a specific condition). On the other hand, for kappa < 0 we do find nonsingular cosmologies. We then move on towards finding static, circularly symmetric line elements with matter obeying (i) p = 0 and (ii) p = rho/2. For p = 0 the solution found is nonsingular for kappa < 0 with the matter-stress-energy representing inhomogeneous dust. For p = rho/2 we obtain nonsingular solutions, for all kappa, and discuss some interesting characteristics of these solutions. Finally, we look at the rather simple p = -rho case where the solutions are either de Sitter or anti-de Sitter or flat spacetime.