The effect of dark matter on the weak cosmic censorship conjecture in the extended space

By analyzing the energy–momentum relationship of the absorbed fermions dropping into a Reissner–Nordstöm–anti-de Sitter black hole surrounded by dark matter, the laws of thermodynamic and weak cosmic censorship conjecture in the extended phase space are investigated. We find that the first law of thermodynamics is valid. However, the validity of the second law of thermodynamics depends on the density [Formula: see text] of the perfect fluid dark matter. In addition, we also find that when the fermions are absorbed, the structures of black hole surrounded by dark matter would not change. Therefore, weak cosmic censorship conjecture holds for the extreme black holes and the non-extreme black holes.

Tidal-charge effects on the superradiance of rotating black holes

The changes a (negative) tidal charge causes at the phenomenon of superradiance which occurs around rotating black holes are investigated. This is made by computing the amplification factors of massless scalar waves being scattered by the black hole. It is shown that the increase of the tidal-charge intensity leads to a considerable enhancement of energy extraction from near-extreme black holes. Such improvement results from the fact that extreme black holes with more negative tidal charges spin faster. Maximum amplification decreases with the increase of the tidal charge intensity if the angular momentum of the black hole per unit mass is fixed. The tidal charge may also change crucially the superradiance phenomenon of massless scalar waves causing maximum amplification to occur for $$m > 1$$ m > 1 differently from the case of Kerr black holes.