Beyond Gravitoelectromagnetism: Critical Speed in Gravitational Motion

Abstract

A null ray approaching a distant astronomical source appears to slow down, while a massive particle speeds up in accordance with Newtonian gravitation. The integration of these apparently incompatible aspects of motion in general relativity is due to the existence of a critical speed. Dynamics of particles moving faster than the critical speed could then be contrary to Newtonian expectations. Working within the framework of gravitoelectromagnetism, the implications of the existence of a critical speed are explored. The results are expected to be significant for high energy astrophysics.

Tidal dynamics in Kerr spacetime

“…However, for V 0 > V c , the probe will accelerate, as treated in detail in [2,5]. In fact, the vertical motion can be described exactly [2,4,5], since equation (61) implies thaṫ…”

“…A general feature of the reduced geodesic (5) is that it contains a critical speed given by 1/ √ 2, especially in the case of one-dimensional motion. The notion of critical speed in gravitational motion has been recently reviewed in [4]. We are particularly interested in the role that the critical speed V c = 1/ √ 2 plays in the motion of the probe; therefore the probe can be launched from m at any initial speed V 0 < 1, but-for simplicity-we concentrate on its motion only when it is relatively close to the reference particle m. Equation (5) to first order in |X| is the generalized Jacobi equation [2] …”

Gravitomagnetic field of rotating rings

“…It is a well known fact that, due to the analogy with electromagnetism (Mashhoon , 2003Mashhoon 2005Mashhoon , 1993Mashhoon et al 2001a;Bini et al 2008), the solution of the field equations (1) can be written in the form…”

Time-varying gravitomagnetism

“…Using the connection coefficients given in [3] for metric (7) with potentials (15), it is straightforward to compute the integral in equation (31) along the unperturbed path of the ray. Thus…”

“…The linear perturbation approach to GEM has been reviewed in [3]. The compact notation of equations (8) and (9) has been employed for simplicity, so that the tensorial character of these equations is purely formal; that is, the background global inertial frame is essentially fixed in this linear GEM treatment.…”