Shadow and deflection angle Reissner – Nordstrom blackhole with cosmological constant in a dark matter fluid - Lobos, Nikko John Leo S. (Animo Repository, 2022)
This study derives and calculates the shadow and the deflection angles of Reissner Nordstrom black hole with the cosmological constant in a dark matter fluid. In the premise of shadow, it is evident that at the observer's current position on Earth, the difference between the black hole shadow in the co-moving and static reference frame is unnoticeable. It shows that the observer is far from the cosmic horizon. The deviation between the two observers requires a susceptible device to detect the difference in the shadow. Using the data from EHT, the calculation shows that the model in this study could retrieve the measured shadow of Sagittarius A* (Sgr A*) by varying the charge $Q$ and dark matter parameter $λ$. However, Messier 87* (M87*) cannot retrieve the value by variation of parameters, $Q$, and $λ$, but the results are still a good approximation. The strong deflection produces a non-physical result at $r \ge 2r_{ps}$. It shows that when the ratio of impact parameter of the closest approach and critical impact parameter significantly deviates from 1, the results are non-physical. As the values of the charge, $Q$, and dark matter fluid, $λ$, increase the strong deflection angle increases. In the case of $Q_{M87*} = Q_{Sgr.A*}$ and $λ_{M87*} = λ_{Sgr.A*}$ the strong deflection for M87* and Sgr. A* at a similar closest approach, $r_{0}$ is approximately equal. It is due to a small difference in the order of magnitude for M87* and Sgr. A*. Weak deflection calculation using the Gauss-Bonnet theorem works in the region far from the black hole. The impact parameter is a scaled value of the black hole mass. Though the increase in charge, $Q$, and dark matter, $λ$ at this region is not that significant compared to the near blackhole case. Applying the conditions $Q_{M87*} = Q_{Sgr.A*}$ and $λ_{M87*} = λ_{Sgr.A*}$ the weak deflection angle at same impact parameter for M87* and Sgr. A* is significantly the same due to the small difference in the order of magnitude for M87* and Sgr. A*. The dark matter fluid, $λ$ shrinks the shadow, photon sphere, and deflection angles while the charge, on the other hand, has fewer effects on the deflection angles but significantly affects black hole shadows.