Shadow and weak deflection angle of extended uncertainty principle black hole surrounded with dark matter

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In this paper, we discuss the possible effects of dark matter on a Schwarzschild black hole with the correction of extended uncertainty principle (EUP), such as the parameter $\alpha$ and the large fundamental length scale $L_*$.

• In particular, we surround 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 $\Delta r_s$.
• In this study, we find 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 show some effects of the EUP parameter on the innermost stable circular orbit (ISCO) radius of time-like particles, photon sphere, shadow radius, and weak deflection angle.