Dehnen halo effect on a black hole in an ultra-faint dwarf galaxy
  There had been recent advancement toward the detection of ultra-faint dwarf
galaxies, which may serve as a useful laboratory for dark matter exploration
since some of them contains almost 99$\%$ of pure dark matter. The majority of
these galaxies contain no black hole that inhabits them. Recently, there had
been reports that some dwarf galaxies may have a black hole within. In this
study, we construct a black hole solution combined with the Dehnen dark matter
halo profile, which is commonly used for dwarf galaxies. We aim to find out
whether there would be deviations relative to the standard black hole
properties which might allow determining whether the dark matter profile in
ultra-faint dwarf galaxies is cored or cuspy. To make the model more realistic,
we applied the modified Newman-Janis prescription to obtain the rotating
metric. We analyzed the black hole properties such as the event horizon,
ergoregion, geodesics of time-like and null particle, and the black hole
shadow. To broaden the scope of this study, we also calculated the weak
deflection angle to examine the effect of the Dehnen profile. Results revealed
that the Dehnen profile causes very tiny but interesting deviations to the
known black hole properties and it shows that the cuspy profile shows more
deviation than the cored profile. In determining whether the dark matter
profile in a dwarf galaxy is cored or cuspy, the implication of the study
revealed the impossibility with the use of present space technology.
