Date of Publication


Document Type

Master's Thesis

Degree Name

Master of Science in Physics

Subject Categories



College of Science



Thesis Advisor

Emmanuel T. Rodulfo

Reggie C. Pantig

Defense Panel Chair

Robert C. Roleda

Defense Panel Member

Al Rey C. Villagracia
Jose Perico H. Esguerra


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 $\lambda$. However, Messier 87* (M87*) cannot retrieve the value by variation of parameters, $Q$, and $\lambda$, 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, $\lambda$, increase the strong deflection angle increases. In the case of $Q_{M87*} = Q_{Sgr.A*}$ and $\lambda_{M87*} = \lambda_{Sgr.A*}$ 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, $\lambda$ at this region is not that significant compared to the near blackhole case. Applying the conditions $Q_{M87*} = Q_{Sgr.A*}$ and $\lambda_{M87*} = \lambda_{Sgr.A*}$ 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, $\lambda$ 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.

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Physical Description

x, 155 leaves


Black holes (Astronomy); Dark matter (Astronomy)

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