Thermodynamics and Shadows of Kerr black holes endowed with a global monopole charge

Abstract: In this article, we present the thermodynamic and shadow properties of rotating black holes with global monopole charge. The angular diameter of Sgr A$^{*}$ black hole is 48.7 $\pm$ 7 $\mu as$, which is 8 $kps$ far away having a mass of $M = 4.0_{-0.6}^{+1.1} \times 10^6 M\odot$ as observed by Event Horizon Telescope and for the M87 black hole, the observed angular diameter is $\theta_d = 42 \pm 3 \mu$as, which is almost $16$ $Mpc$ far away with a mass of $M = (6.5 \pm 0.7) \times 10^9 M_\odot$. The global monopole charge parameter $\alpha$ strongly affects the shape and size of the black hole shadow. We derived all the necessary equations to obtain the angular diameter of the rotating black hole shadow with the effect of the global monopole charge parameter $\alpha$. For $\alpha$ $\in$ (0, 0.08) with $a$ $\in$ $(0.7 M, 0.99 M)$, the angular diameter of M87 black hole shadow varies from $39$ $\mu as$ to $51$ $\mu as$. The angular diameter of Sgr A$^{*}$ black hole with global monopole charge parameter $\alpha$ $\in$ (0, 0.04) and $a$ $\in$ $(0.7 M, 0.99 M)$, varies from $50$ $\mu as$ to $55$ $\mu as$. For bound values of $\alpha$ and $a$, our results are consistent with the EHT observations.