Black hole solution and strong gravitational lensing in Eddington-inspired Born-Infeld gravity

TL;DR

This paper derives a charged black hole solution in Eddington-inspired Born-Infeld gravity and analyzes how the theory's parameters influence strong gravitational lensing, offering potential observational tests for this alternative gravity model.

Contribution

It presents the first charged black hole solution with a cosmological constant in EiBI gravity and explores its lensing properties, highlighting the effects of the coupling parameter on observable phenomena.

Findings

Positive coupling parameter reduces black hole horizon and photon sphere size.

Coupling parameter decreases angular position and magnification of relativistic images.

Increases angular separation between images, aiding potential observational tests.

Abstract

A new theory of gravity called Eddington-inspired Born-Infeld (EiBI) gravity was recently proposed by Ba\~{n}ados and Ferreira. This theory leads to some exciting new features, such as free of cosmological singularities. In this paper, we first obtain a charged EiBI black hole solution with a nonvanishing cosmological constant when the electromagnetic field is included in. Then based on it, we study the strong gravitational lensing by the asymptotic flat charged EiBI black hole. The strong deflection limit coefficients and observables are shown to closely depend on the additional coupling parameter $\kappa$ in the EiBI gravity. It is found that, compared with the corresponding charged black hole in general relativity, the positive coupling parameter $\kappa$ will shrink the black hole horizon and photon sphere. Moreover, the coupling parameter will decrease the angular position and relative magnitudes of the relativistic images, while increase the angular separation, which may shine new light on testing such gravity theory in near future by the astronomical instruments.