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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,-1) Friedmann-Roberston-Walker universes with (i) pressureless dust (P=0) and (ii) perfect fluid (P=ρ/2), as matter sources. When the theory parameter κ>0, our cosmological solutions are generically singular (except for the open universe, with a specific condition). On the other hand, for κ<0 we do find non-singular cosmologies. We then move on towards finding static, circularly symmetric line elements with matter obeying (i) p=0 and (ii) p=ρ/2. For p=0, the solution found is nonsingular for κ<0 with the matter--stress--energy representing inhomogeneous dust. For p=ρ/2 we obtain nonsingular solutions, for all κ, and discuss some interesting characteristics of these solutions. Finally, we look at the rather simple p=-ρcase where the solutions are either de Sitter or anti-de Sitter or flat spacetime.