The effect of frame-dragging (i) in Kerr naked singularities and (ii) on accretion discs around the rotating compact objects

 In the first part of my talk, I shall discuss a specific criterion to decide
on the existence or otherwise of Kerr naked singularities, as opposed to a black hole,
in terms of the precession frequency behavior of a test gyroscope due to the
frame-dragging effect. Specifically, if we lower the gyro along the polar axis of a Kerr
black hole, the precession frequency becomes arbitrarily high, blowing up as the event
horizon is approached. On the other hand, in the case of naked singularity, this
frequency remains always finite and well-behaved. An intriguing behavior is, in the Kerr
naked singularity case, the precession frequency of the gyro is directly proportional to
the distance `r' after reaching a maximum, in the limit of r = 0, as opposed to 1/r^3
dependence in all other astrophysical cases.
In the second part of my talk, I shall discuss a steady state warped disc solution
around compact objects. An expression of the tilting angle of a thin accretion disc
around a rotating compact object is derived without neglecting the inner-edge boundary
condition. We show that the inner disc is not necessarily to be aligned always along the
equator rather a finite inclination with respect to the equator may occur in some cases.
Interestingly, the inner edge of the accretion disc may be tilted at a greater angle to
the compact object than the outer parts of the disc, depending on the disc properties.
It is also shown that the disc is tilted due to only the viscosity of accreting material
even when the frame-dragging effect vanishes, which may occur in a static spherically
symmetric spacetime.