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

TL;DR

This paper investigates how a global monopole charge influences the thermodynamics and shadow characteristics of rotating Kerr black holes, providing equations and results consistent with observations of Sgr A* and M87 black holes.

Contribution

It introduces the effect of a global monopole charge on black hole shadows and thermodynamics, deriving relevant equations and analyzing observational consistency.

Findings

Global monopole charge significantly alters black hole shadow size and shape.

Derived equations enable calculation of shadow diameters considering monopole effects.

Results align with Event Horizon Telescope observations for specific parameter ranges.

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.