On the unphysical nature of gravitomagnetic waves

The equivalence principle and the gravitomagnetic Larmor theorem are formulated on the basis of the validity of the hypothesis of locality. This hypothesis posits the local equivalence of an accelerated observer with a momentarily comoving inertial observer. Mashhoon demonstrated that locality is inherently limited by the acceleration length associated with an accelerated observer. On the basis of the equivalence principle and of the gravitomagnetic Larmor theorem, one can assimilate the orthogonal gravitational and gravitomagnetic fields of a gravitomagnetic wave oscillating with a given frequency to the centripetal acceleration and angular velocity of a frame attached to an ideal massless torsion pendulum oscillating with the same frequency. In the limit of rotational speeds approaching the speed of light, one shows that the acceleration length of the oscillating rotating system is null. Since this limit case is equivalent to the propagation of gravitomagnetic waves (propagating at the speed of light) this result is interpreted as indicating that gravitomagnetic waves propagating with the speed of light in vacuum are unphysical. It is further shown that superluminal propagation speeds are also excluded on the basis that they do not allow for any induction between gravitomagnetic and gravitational fields. Gravitomagnetic waves propagating with a universal sub-luminal speed are also ruled out. For this particular case, it is shown that the gravitomagnetic wave quanta of energy cannot be absorbed or emitted by a mechanical or an electromagnetic oscillator, thus making their detection or production impossible.