The Precession of Gyroscope in the Vicinity of Black Hole and Naked Singularity

Majumder, Paulami (2026) The Precession of Gyroscope in the Vicinity of Black Hole and Naked Singularity. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (Phd thesis of Paulami Majumder (18RS040)) 18RS040.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

In this thesis, we investigate the precessional motion of a gyroscope in the intense gravitational environments surrounding black holes and naked singularities. The phenomenon of gyroscopic precession provides an insightful method for probing the curvature and rotational structure of spacetime. Within the framework of Einstein’s general relativity, the spin axis of a gyroscope moving through curved spacetime experiences a precession with respect to distant inertial frames—a wellknown relativistic effect. This precession has been measured in weak gravitational fields, as verified by the Gravity Probe B experiment, which confirmed the geodetic and frame-dragging effects around Earth with remarkable precision. However, the corresponding behaviour of gyroscopic precession in regions of strong gravity— particularly near black holes and naked singularities—remains far less understood. A more profound comprehension of precession frequencies in such extreme regimes can aid in distinguishing various compact objects and in testing general relativity’s predictions under strong-field conditions. This work primarily examines gyroscopic precession in both static and rotating gravitational backgrounds, encompassing black holes and naked singularities. To describe this motion, we employ the fully covariant Frenet–Serret formalism, introduced by Iyer and Vishveshwara, which enables the analysis of a gyroscope following an arbitrary timelike trajectory. The spacetime curvature and precession characteristics are represented using the Frenet–Serret scalars κ, τ1, and τ2. Within this theoretical framework, the precession behaviour is studied for Schwarzschild, Schwarzschild–Anti-de Sitter, Reissner–Nordstr¨om, and Kerr geometries, using both standard coordinate systems and the horizon-penetrating Kerr–Schild form to eliminate coordinate singularities. Our analysis shows that the apparent divergence of the precession frequency in strong gravitational fields—most notably when approaching the event horizon in black hole spacetimes—is a consequence of coordinate degeneration rather than a genuine physical effect. The precession frequency remains finite for all physically admissible timelike trajectories. In Reissner–Nordstr¨om spacetimes, both black holes and naked singularities yield finite precession near the horizon, yet a reversal of frequency along null geodesics offers a distinguishing signature. In the Kerr case, distinct behaviours emerge between co-rotating and counter-rotating observers, while the over-spinning case (a > M), representing a naked singularity, reveals novel precession patterns. These results highlight that gyroscopic precession serves as an effective probe of spacetime geometry, though it does not directly indicate the existence of an event horizon. The outcomes of this study have further significance for gravitational-wave astrophysics, particularly in the modelling of extreme mass-ratio inspirals (EMRIs) relevant to upcoming observatories like LISA.

Actions (login required)

View Item