The phenomenological study on alternative black holes and dark matter distribution

Black holes and dark matter stand out as two of the most intriguing and mysterious subjects in modern physics. Significant progress has been made in understanding black holes through gravitational waves and imaging observations. However, due to the precision limitations of observations, we can not exclude the possibility of alternative black holes beyond general relativity. Moreover, general relativity itself faces challenges, such as the spacetime singularity problem. Therefore, there is a need for more phenomenological studies on alternative black holes, enabling potential comparisons with observations. Concerning dark matter, numerous outstanding simulations aim to address the distribution of dark matter by assuming the collisionless nature of dark matter particles. Several universal properties of dark matter halos have been observed. Unfortunately, a satisfactory theory to predict these properties is lacking. Consequently, there is a quest for a phenomenological model that can provide a unified description of the observed empirical laws in simulations and also inspire theoretical investigations.
In this thesis, we employ several phenomenological studies on both black holes and dark matter distributions.
We consider two alternative black holes: the rotating regular black hole and the rotating hairy black hole, corresponding to the violation of two theorems in general relativity, namely the singularity theorem and the no hair theorem, respectively. The scalar field was investigated around the rotating regular black hole, while the gravitational field was studied in the regime of the rotating hairy black hole. These investigations allow us to discuss the phenomenology of superradiance and quasinormal modes around these two alternative black holes. Additionally, we also study the energy extraction from these two alternative black holes via magnetic reconnection. The effects of the new parameters, which characterize the deviation from Kerr black holes, were presented, and the physical implications were also discussed.
For dark matter distribution, we propose and analyze a new phenomenologi- cal model of dark matter phase space distribution, which could semi-analytically provide NFW-like density profile and analytically give velocity magnitude as well as components distributions that closely align with simulation data. Particularly noteworthy is the ability of our model that could accurately capture radial velocity data across the entire velocity range and the lower velocity regime of tangential data. While certain discrepancies exist, our model demonstrates strong predictive performance in reproducing universal properties observed in simulations. These results suggest that our model may be relevant for describing the distribution of dark matter particles.