Born-Infeld gravity coupled to Born-Infeld electrodynamics

TL;DR

This paper explores how Born-Infeld modifications in both gravity and electrodynamics affect black hole solutions, photon trajectories, and gravitational lensing, revealing new features and potential observational signatures.

Contribution

It provides the first detailed analysis of spherically symmetric solutions in coupled Born-Infeld gravity and electrodynamics, including classifications and comparisons with known limits.

Findings

Black hole and naked singularity solutions depending on parameters

Photon sphere radius increases with parameter ta

Positive correction to weak lensing deflection angle

Abstract

We investigate spherically symmetric, static spacetimes in Eddington-inspired Born-Infeld gravity coupled to Born-Infeld electrodynamics. The two constants, $b^2$ and $\kappa$ which parametrise the Born-Infeld 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 $\kappa$, as well as charge and mass. Several such solutions are classified and understood through the analysis of the associated metric functions for fixed $\kappa$, varying $b^2$ and vice-versa. Further, we also compare the new metric functions with those for the known $b^2\rightarrow \infty$ (Maxwell) and the $\kappa \rightarrow 0$ (geonic black hole) cases. Interestingly, for a particular relation between these two parameters, $b^2=1/{4\kappa},\, \kappa >0$, we obtain a solution resembling the well-known Reissner-Nordstr\" om 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 $\kappa$ and $(ii)$ a net positive contribution in the leading order correction term involving $\kappa$, 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.