LENSE-THIRRING PRECESSION BY BLACK HOLES IN THE RANDALL-SANDRUM MODEL

Abstract

The description of our universe on a brane suggests a large extra dimension and a fundamental scale of gravity, which can be several orders of magnitude lower than the Planck scale. An interesting consequence of the brane world scenario is the nature of spherically symmetric vacuum solutions of the brane gravitational field equations, which can represent black holes with properties quite different from those of ordinary black holes in 4 dimensions. The paper investigates the Lense-Thirring precession by black holes in the Randall-Sandrum model caused by the frame-dragging effect. Lense-Thirring precession is a general relativistic effect that occurs when a rotating particle is displaced vertically from the equatorial axis of a rotating body in such a way that the framedragging causes oscillations around the ecliptic and periapsis. The Randall-Sandrum model assumes that our universe is a negative tension domain wall separated from the positive tension wall by an anti-de Sitter space slab. The space-time of a black hole in the Randall-Sandrum model of the "brane world" theory is characterized by an induced tidal charge. In particular, a generalized expression for the Lense-Thirring precession rate in the case of a strong and weak gravitational field is obtained. Further, the precession of the gyroscope in the plane θ=0 is considered, the dependence of the Lense-Thirring precession rate for a stellar-mass black hole and a supermassive black hole is shown for different values of the tidal charge β. The results of numerical simulation are presented for various values of the tidal charge and the radial coordinate.