Abstract:
Recent astronomical observations predict the accelerating expansion of the universe,
which could be due to a cosmological constant or quintessence field. Some other observations
suggest the existence of dark matter in many astrophysical phenomena such
as galactic rotation curves and the galaxy cluster dynamics. In this thesis, the rotating
black holes and naked singularities in the quintessence field and perfect fluid
dark matter have been studied. The critical values of the spin, quintessential field, and
perfect fluid matter parameters, to differentiate black holes from naked singularities,
have been presented. Due to the rotation of the central object the spacetime exhibits
effects of the spin precession which causes the dragging of locally inertial frames along
the rotating spacetime. The precession of a test gyroscope has been studied and used
to differentiate the black holes from naked singularities. If the precession frequency of
a test gyroscope blows up as it approaches the central object along any direction, the
object is a black hole. If it remains finite everywhere, then the object is a naked singularity.
The black holes in the external magnetic field is also a topic of great interest for
researcher. The charge black hole in the external magnetic field produces rotational
effects on spacetime. The effect of the external magnetic field on the frame dragging
effects due to the rotation of the central object has also been studied.
