Time-varying gravitomagnetism

Abstract

Time-varying gravitomagnetic fields are considered within the linear postNewtonian approach to general relativity. A simple model is developed in which the gravitomagnetic field of a localized mass-energy current varies linearly with time. The implications of this temporal variation of the source for the precession of test gyroscopes and the motion of null rays are briefly discussed.

Gravitomagnetic time-varying effects on the motion of a test particle

“…Time-varying GEM fields can be interesting in actual astrophysical events: for instance when a star, or a planet, loses its spin angular momentum, it generates a time-varying GM field, whose effects on the neighboring objects can be evaluated. As an example, one may consider the decrease of the rotation rate of the Earth (due to tidal effects): this corresponds to a loss of angular momentum which, in turn, produces a time-dependent GM field; however, this variability is so small that is not expected to influence experiments aimed at the measurement of the GM field of the Earth, such as GP-B [8,9].…”

Post-Newtonian approximation in Maxwell-like form

“…In the half century since then, this Maxwell-like formulation and variants of it have been widely explored and used; see, e.g., [6,7,8,9,10,11,12,13] and references therein.…”

Time-varying Lense–Thirring system

“…Astronomical bodies in general rotate; however, the magnitude of the proper angular momentum is seldom constant. In two recent papers [3,4], the gravitational physics around a rotating central source whose spin angular momentum vector is fixed in space but varies linearly in time has been explored. In particular, it has been shown in [3] that sufficiently far from such a source, the spacetime metric is given by…”

“…Here, r = |x|, M is the mass of the source and its angular momentum is given by [3,4], we simply ignore the processes by which the variation of angular momentum is turned on and off and assume that equation (4) holds throughout the temporal interval of interest; furthermore, all radiative effects are neglected.…”

“…As demonstrated in [3,4], equation (2) represents the metric of a nonstationary linearized Kerr spacetime. The geodesic equation in Kerr spacetime is completely integrable [5]; more recent results are contained, for instance, in [6] and references therein.…”