Spin precession in a black hole and naked singularity spacetimes

Understand

We propose here a specific criterion to address the existence or otherwise of Kerr naked singularities, in terms of the precession of the spin of a test gyroscope due to the frame dragging by the central spinning body.

• We show that there is indeed an important characteristic difference in the behavior of gyro spin precession frequency in the limit of approach to these compact objects, and this can be used, in principle, to differentiate the naked singularity from black hole.
• Specifically, if gyroscopes are fixed all along the polar axis upto the horizon 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.