The effect of dark matter on schwarzschild and kerr black holes: Considerations on the weak deflection angles and the kerr shadow

• Main Author: Pantig, Reggie C.
• Format: text
• Language: English
• Published: Animo Repository 2020
• Subjects: Schwarzschild black holes; Kerr black holes; Dark matter (Astronomy); Physics
• Online Access: https://animorepository.dlsu.edu.ph/etd_doctoral/1406; https://animorepository.dlsu.edu.ph/cgi/viewcontent.cgi?article=2447&context=etd_doctoral
• Institution: De La Salle University

We consider the effect of a spherical dark matter distribution that surrounds a black hole of mass m. The dark matter is only characterized by its mass M, inner radius rs , and thickness ∆rs . A black hole surrounded by an astrophysical environment such as dark matter is called a dirty black hole. Considering first the dirty Schwarzschild black hole, we calculated the weak deflection angle using the [Ishihara et al., 2016] method, which considers the finite distance of the source and the receiver from the black hole. We found out the for notable deviation on the weak deflection to occur, the dark matter thickness is estimated to be ∆rs ∼ 2 √ 3mM. This implies that the weak deflection angle of a Schwarzschild black hole cannot be used to detect dark matter inside one’s galaxy unless the dark matter is distributed near it for a given value of M. Further in this study is the use of the Newman-Janis algorithm to extend the dirty Schwarzschild black hole to rotating dirty Kerr black hole. Findings indicate that considerable deviations in the horizons, null orbits, shadow radius, and its corresponding observables require high dark matter density. We also find that time-like orbits are very sensitive to deviation even if the dark matter mass to thickness ratio is estimated to be less than 10 percent. Moreover, the location where the Penrose process occurs remains uninfluenced by dark matter. The deviation in the energy emission rate indicates that dark matter tends to reduce the lifetime of a black hole. Finally, the analytic estimate for ∆rs in dirty Kerr black hole is obtained using the deviation in the weak deflection angle. Findings reveal that ∆rs for the slow-spin limit is greater than the ultra-relativistic limit. It implies that the rotation of black hole does not improve the value of ∆rs . In either case, however, these conditions are still not satisfied within our galaxy. Index Terms—Dirty black hole; Dark matter; Gauss-Bonnet theorem; Weak deflection angle; Finite-distance; Newman-Janis algorithm; Black hole shadow; Hamilton-Jacobi formalism.