Strong field gravitational lensing by hairy Kerr black holes

TL;DR

This paper extends the analysis of strong gravitational lensing to hairy Kerr black holes, revealing how deviations from standard Kerr solutions affect lensing observables and their potential detectability with current telescopes.

Contribution

The study generalizes gravitational lensing formalism to hairy Kerr black holes, introducing deviation parameters and analyzing their effects on lensing characteristics compared to standard Kerr black holes.

Findings

Deflection coefficient $ar{a}$ increases with $eta$ and decreases with $ ilde{eta}$.

Angular position $ heta_{ ext{infinity}}$ decreases with $eta$.

Deviations in angular positions are below current observational resolution.

Abstract

Recent times witnessed a surge of interest in strong gravitational lensing by black holes due to the Event Horizon Telescope (EHT) results, which suggest comparing the black hole lensing in general relativity and modified gravity theories. This may help us to assess the phenomenological differences between these models. A Kerr black hole is also a solution to some alternative theories of gravity, while recently obtained modified Kerr black holes (hairy Kerr black holes), which evade the no-hair theorem, are due to additional sources from surrounding fluid, like dark matter, having conserved energy momentum tensor (EMT). These hairy Kerr black holes may also be solutions to an alternative theory of gravity. We generalize previous work on gravitational lensing by a Kerr black hole in the strong deflection limits to the hairy Kerr black holes, with a deviation parameter $\alpha$ and a primary hair $\ell_0$. Interestingly, the deflection coefficient $\bar{a}$ increases and decreases with increasing $\ell_0$ and $\alpha$ respectively. $\bar{b}$ shows opposite behaviour with $\ell_0$ and $\alpha$. We also find that the deflection angle $\alpha_D$, angular position $\theta_{\infty}$ and $u_{m}$ decrease, but angular separation $s$ increases with $\alpha$. We compare our results with those for Kerr black holes, and also apply the formalism to discuss the astrophysical consequences in the context of the supermassive black holes Sgr A* and M87*. We observe that the deviations of the angular positions from that of the Kerr black hole are not more than $2.6~\mu$as for Sgr A* and $1.96~\mu$as for M87*, which are unlikely to be resolved by the current EHT observations.