We investigate spherically symmetric, static spacetimes in Eddington-inspired Born-Infeld gravity coupled to Born-Infeld electrodynamics. The two constants, b 2 and κ which parametrise the BornInfeld structures in the electrodynamics (matter) and gravity sectors, characterise the features of our analytical solutions. Black holes or naked singularities are found to arise, depending on the values of b 2 and κ, as well as charge and mass. Several such solutions are classified and understood through the analysis of the associated metric functions for fixed κ, varying b 2 and vice-versa. Further, we also compare the new metric functions with those for the known b 2 → ∞ (Maxwell) and the κ → 0 (geonic black hole) cases. Interestingly, for a particular relation between these two parameters, b 2 = 1/4κ, κ > 0, we obtain a solution resembling the well-known Reissner-Nordström line element, albeit some modifications. Using this particular solution as the background spacetime, we study null geodesics for Born-Infeld photons and also, gravitational lensing. Among interesting features we note (i) an increase in the radius of the photon sphere with increasing κ and (ii) a net positive contribution in the leading order correction term involving κ, in the weak lensing formula for the deflection angle. We also investigate the effective potential and light propagation for various other solutions through numerics and plots. In summary, our work is the first attempt towards figuring out how Born-Infeld structures in both the matter and gravity sectors can influence the nature and character of resulting gravitational fields. * soumyajana@phy.iitkgp.ernet.in, sayan@iitkgp.ac.in 2
The observations of gravitational waves from the binary neutron star merger event GW170817 and the subsequent observation of its electromagnetic counterparts from the gamma-ray burst GRB 170817A provide us a significant opportunity to study theories of gravity beyond general relativity. An important outcome of these observations is that they constrain the difference between the speed of gravity and the speed of light to less than 10 −15 c. Also, the time delay between the arrivals of gravitational waves at different detectors constrains the speed of gravity at the Earth to be in the range 0.55c < vgw < 1.42c. We use these results to constrain a widely studied modified theory of gravity: Eddington-inspired Born-Infeld (EiBI) gravity. We show that, in EiBI theory, the speed of gravitational waves in matter deviates from c. From the time delay in arrival of gravitational wave signals at Earth-based detectors, we obtain the bound on the theory parameter κ as |κ| 10 21 m 2 . Similarly, from the time delay between the signals of GW170817 and GRB 170817A, in a background Friedmann-Robertson-Walker universe, we obtain |κ| 10 37 m 2 . Although the bounds on κ are weak compared to other earlier bounds from the study of neutron stars, stellar evolution, primordial nucleosynthesis, etc., our bounds are from the direct observations and thus worth noting.
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 = 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 matterstress-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 = −ρ case where the solutions are either de Sitter or anti-de Sitter or flat spacetime.
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