Linear frame dragging along one spatial dimension

Abstract

Inertial dragging is a well-known effect described within the framework of General Relativity. Notwithstanding, some fundamental questions related to its nature still deserve attention. One of these, rooted in Mach’s principle, wonders whether the inertial mass of particles could be due to the relative motion with respect to other particles. To tackle this question, we study the inertial dragging resulting in a test particle located in the centre of mass of two faraway masses accelerating in the same direction. In this simple setup, calculations show the appearance of an inertial force, which entails the test particle accelerating in the opposite direction. Therefore, the proposed model shows that relative accelerations of distant masses with respect to a test particle induce inertial dragging effects which are similar to the inertia corresponding to an acceleration of the test particle itself. This could be suggestive of a more concrete interpretation of Mach’s principle which would imply that the gravitational constant may be the approximate value of a more complex inertial field.