Rotational gravitoelectromagnetism

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Rotational gravitoelectromagnetic effects are the dragging effects (or spacetime distortion effects) that are expected to appear when a body rotates with respect to its environment.

Effects

There are two main classes of GEM effect associated with rotation:

  • sideways dragging effect, and
  • a radial effect.

Both appear in Twentieth Century gravitational theory, and can be derived from Mach's principle.

Machian derivation of the transverse GEM effect

Suppose that we stand at the Earth's equator, and launch a space-rocket, straight up.

after it has left the Earth's influence, an observer drifting in deep space should see the rocket appear to be travelling in practically a straight line with respect to the background stars .

However, to us standing on the equator, the reference system provided by the background starfield appears to rotate around us once every 24 hours, moving from East to West. If our rocket eventually moves in a straight line wrt this starfield, then we must see it appearing to veer Westward after it has been launched , so that we end up seeing it passing overhead once every 24 hours, in lockstep with the starfiels.

While there is no difficulty explaining the rocket's behaviour from the viewpoint of view of the deep-space observer, the Machian explanation of what we see is that, for us, the rocket is being deflected westwards by a gravitational effect associated with the rotation of the surrounding starfield.

If there is nothing special or unique about the matter making up these stars, we can extrapolate from the Machian observation to make a more general prediction:

  • A hollow rotating massed shell should create dragging forces within it that pull contained matter and light around in the direction of rotation.

This may seem like not a very useful prediction to make, as we are not in the habit of constructing giant hollow spheres from quantities of matter measured in solar masses. However, we can use topological arguments to "turn the experiment inside out" – we normally think of the Earth' surface as being contained within the universe and pointing outwards, and the background stars as being equivalent to a hollow spherical shell facing inwards. we can, though, create an artificial geometrical remapping that describes the Earth on the outside facing in, and the starfield as an outward-facing rotating ball of matter. In this artificial description, a central rotating mass is associated with a sideways gravitational dragging effect, and if the same basic laws of physics apply in all systems, then this sideways dragging around a rotating mass should also apply in more sane coordinate systems, when we look at the physics of a rotating star or planet.

We can also apply the principle of mutuality - if the rotating background universe exerts a drag on the Earth, then the rotating Earth should also apply a (far weaker!) drag on the distant stars. this gives us a second behaviour:

  • A solid rotating mass should create dragging forces around it that pull contained matter and light around in the direction of rotation.

Experimental verification

To test the dragging prediction, NASA funded the Gravity Probe B experiment, which launched in 2004. GP-B placed four exquisitely-engineered gyroscopes in polar orbit, to measure the variation in alignment as the satellites orbited. In "old" Newtonian physics, the satellites should align based purely on their motion relative to the background stars ... in the GP-B result, the satellites' sense of what constituted "a non-rotating frame" was dominated by the influence of the background starfield, but the rotation of the Earth's mass beneath the gyroscopes also had an effect (see: Democratic principle).

Radial effect

In our "rocket" example, the Earth's rotation helps to "hurl" the rocket free of the Earth's gravitational field, so the the rocket needs less fuel to escape Earth-gravity (this is why rocket-launching sits tend to be situated as near as possible to the equator).

In the Machian description, physics as seen by an observer standing at the equator reveals the rocket managing to get into space more easily because of an outward-pointing gravitational field associated with the rotation of the starfield:

  • A hollow rotating massed shell should create a gravitational effect pulling light and matter directly away form the rotation axis, and increasing in strength roughly as a function of the distance from the axis.

Once again, the initial prediction does not seem particularly useful, and just seems ot give a more complicated way of describing the effects that we already know.

But once again, we can apply topology and/or the principle of mutuality to obtain a more useful effect:

  • A solid rotating mass should create an additional inward attraction, acting at right angles to its rotation axis. *

So, a spinning star creates a twist in the paths of nearby moving matter and light, and also has an enhanced attraction due to its rotation (which can be thought of as the gravitational effect of the star's kinetic energy).

External links:

Notes

  • The combination of the radial and transverse effects means that small surrounding objects aren't attracted towards the star's exact centre, or to the exact position of its rotation axis, but to positions offset sideways from the central axis, in the direction of motion of the star's nearest parts (see: Kerr singularity).