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=ρ2), 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 nonsingular cosmologies. We then move on towards finding static, circularly symmetric line elements with matter obeying (i) p=0 and (ii) p=ρ2. For p=0, the solution found is nonsingular for κ<0 with the matter-stress-energy representing inhomogeneous dust. For p=ρ2 we obtain nonsingular solutions, for all κ, and discuss some interesting characteristics of these solutions. Finally, we look at the rather simple p=-ρ case where the solutions are either de Sitter or anti–de Sitter or flat spacetime.

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13 pages, 8 figures, revised, corrected and extended version

04.50.Kd
04.20.Jb
04.20.-q
dimension: 3
space-time: dimension
gravitation
numerical calculations
cosmological model
Robertson-Walker
pressure

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