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تسجيل مستخدم جديدShadow and weak deflection angle of extended uncertainty principle black hole surrounded with dark matter
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We discussed the possible effects of dark matter on a Schwarzschild black hole with extended uncertainty principle (EUP) correction such as the parameter $alpha$ and the large fundamental length scale $L_*$. We surrounded the EUP black hole of mass $m$ with a static spherical shell of dark matter described by the parameters mass $M$, inner radius $r_s$, and thickness $Delta r_s$. Considering only the case where the EUP event horizon coincides $r_s$, the study finds that there is no deviation in the event horizon, which readily implies that the black hole temperature due to the Hawking radiation is independent of any dark matter concentration. In addition, we explored the deviations in the innermost stable circular orbit (ISCO) radius of time-like particles, photonsphere, shadow radius, and weak deflection angle. It is found that time-like orbits are sensitive to deviation even for low values of mass M. A greater dark matter density is needed to have considerable deviations to null orbits. Using the analytic expression for the shadow radius and the approximation $Delta r_s>>r_s$ revealed that $L_*$ should not be any lower than $2m$. To broaden the scope of this study, we also calculated the analytic expression for the weak deflection angle using the Ishihara method to improve the dark matter estimate found via shadow radius. As a result, the estimate improved by a factor of $(1+4alpha m^2/L_*^2)$ due to the EUP correction parameters. The estimates for the shadow radius and weak deflection angle are compared using the estimated values of galactic mass, and the mass of the supermassive black hole (SMBH) at the center of Sgr A* and M87 galaxies. We found out that the analytical estimates are not satisfied in these galaxies, which indicates that the notable deviation due to dark matter is only evident and considerable if the dark matter distribution is near the supermassive black hole.
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In this paper, we present the weak deflection angle in a Schwarzschild black hole of mass $m$ surrounded by the dark matter of mass $M$ and thickness $Delta r_{s}$. The Gauss-Bonnet theorem, formulated for asymptotic spacetimes, is found to be ill-be
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