Weak deflection angle and shadow of an extended uncertainty principle black hole with dark matter halo

This study calculates the weak deflection angle of light rays and the shadow of an extended uncertainty principle (EUP) black hole with dark matter halo. The finite-distance form of the weak deflection angle was determined following Ishihara et al. The EUP correction increases the weak deflection angle of light rays, independent of the dark matter halo. For an M87* SMBH, the EUP gives a significant correction of ≈2.08×10^−7 rad to the Schwarzschild case of ≈4×10^−6 rad, or about 5% correction. Its effect is significantly larger than the dark matter halo by 22 orders of magnitude. The shadow of an EUP blackhole with dark matter halo was determined following Perlick et al. and Konoplya. The EUP correction gives a significant increase in the shadow radius of about 2.6×10^12 m to the Schwarzschild case of ≈5.01×10^13 m, or about 5% correction. The shadow angular radius was fit to the observed value of α_sh ≈21 μas by the EHT [1]. The free parameters of the system were determined: Dark matter thickness ∆rs = 1.76×10^32 m and EUP parameter α = 0.014. This study hopes to provide deeper insight into the macroscopic effects of quantum gravity, particularly its role in the interplay between black holes and dark matter