TY - JOUR

T1 - Shadow and weak deflection angle of extended uncertainty principle black hole surrounded with dark matter

AU - Pantig, Reggie C.

AU - Yu, Paul K.

AU - Rodulfo, Emmanuel T.

AU - Övgün, Ali

N1 - Funding Information:
We are very grateful to the anonymous referee, whose insightful comments and suggestions contribute to the betterment of this paper.
Publisher Copyright:
© 2021 Elsevier Inc.

PY - 2022/1

Y1 - 2022/1

N2 - 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 α 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 rs, and thickness Δrs. 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. It is found that time-like orbits are affected by deviation of low values of mass M. A greater dark matter density is needed to have remarkable effects on the null orbits. Using the analytic expression for the shadow radius and the approximation Δrs>>rs, it is revealed that L∗ should not be lower than 2m. To broaden the scope of this study, we also calculate the analytic expression for the weak deflection angle using the Ishihara et al. method (Ishihara et al., 2016). As a result, we show that Δrs is improved by a factor of (1+4αm2/L∗2) due to the EUP correction parameters. The calculated shadow radius and weak deflection angle are then compared using the estimated values of the galactic mass from Sgr A*, M87, and UGC 7232, as well as the mass of the supermassive black hole at their center.

AB - 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 α 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 rs, and thickness Δrs. 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. It is found that time-like orbits are affected by deviation of low values of mass M. A greater dark matter density is needed to have remarkable effects on the null orbits. Using the analytic expression for the shadow radius and the approximation Δrs>>rs, it is revealed that L∗ should not be lower than 2m. To broaden the scope of this study, we also calculate the analytic expression for the weak deflection angle using the Ishihara et al. method (Ishihara et al., 2016). As a result, we show that Δrs is improved by a factor of (1+4αm2/L∗2) due to the EUP correction parameters. The calculated shadow radius and weak deflection angle are then compared using the estimated values of the galactic mass from Sgr A*, M87, and UGC 7232, as well as the mass of the supermassive black hole at their center.

KW - Black holes

KW - Deflection angle

KW - Gauss–Bonnet theorem

KW - Shadow cast

KW - Weak gravitational lensing

UR - http://www.scopus.com/inward/record.url?scp=85121287904&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2021.168722

DO - 10.1016/j.aop.2021.168722

M3 - Article

AN - SCOPUS:85121287904

VL - 436

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

M1 - 168722

ER -