Modelling the Sgr A${}^{\ast }$ and M87${}^{\ast }$ shadows by using the Kerr-Taub-NUT metrics in the presence of a scalar field

Abstract

The recent unveiling of the images of Sgr A* and M87* has significantly advanced our understanding of gravitational physics. In this study, we derive a class of Kerr-Taub-NUT metrics in the presence of a scalar field (KTNS). Treating these metrics as models for supermassive objects, we constrain the parameters using shadow size estimates done by observations of M87* and Sgr A* from the Event Horizon Telescope (EHT). Comparing the obtained results with M87* data, we show an upper limit on the NUT charge $n$ such that the constraint on the shadow deviation from circularity ($\Delta C$) will be fulfilled for $n<0.5$, and this allowed range changes with a variation in other parameters. Additionally, our findings reveal that fast-rotating KTNS metrics are better candidates for supermassive M87* than slowly rotating ones. We continue our study by estimating parameters using Keck and VLTI observations of Sgr A* and find that the constraint on the fraction deviation $\delta$ is maintained within a certain range of the NUT charge such that the Keck bound is satisfied for $n<0.41$. In contrast, the VLTI bound can be fulfilled for $n>0.34$. Finally, we investigate weak gravitational lensing using the Gauss-Bonnet theorem and illustrate that all model parameters increase the deflection angle, causing light rays to deviate more significantly near fast-rotating KTNS objects.

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