# Lorentz transformed gravity?

1. Jun 22, 2014

### DrZoidberg

A lorentz transformed electric field has it's own name. It's called a magnetic field.
That makes me wonder if there is a name for a lorentz transformed gravity field?
Also is it theoretically possible to build a "gravity transformer"? i.e. a transformer that uses moving mass instead of electric charges and makes use of lorentz transformation in the same way as an electromagnetic transformer does?

2. Jun 22, 2014

### pervect

Staff Emeritus
A lorentz transformed electric field has in general magnetic parts and electric parts, so I wouldn't put things quite the way you did.

There are a couple of names for the gravitational analogue of the magnetic field. One is the graviitomagnetic field, as part of a weak-field approximation to general realtivity usually called GEM. http://en.wikipedia.org/w/index.php?title=Gravitoelectromagnetism&oldid=611677107

Another more common name is "frame dragging"

As far as building a "gravity transformer", I'm not aware of any equivalent of Ohm's law or a that would result in the gravitational equivalent of an electrical conductor, nor of any gravitational equivalent of an iron core for magnetic fields. So I suspect it will be difficult if not impossible, similar to the task of building a transformer without either windings or a core.

One might be able to generate frame-dragging effects with hyper-dense fluids circulating at relativistic velocities, though.

I believe Robert Forward considered systems of the later sort. I don't recall enough to remember if there were any useful analogies to a transformer, the intent was some sort of exotic propulsion system as I recall.

3. Jun 22, 2014

### WannabeNewton

Things are a lot more subtle for gravity. First of all, how are you defining "gravitational field"? Is this in the context of SR or GR? In GR the term has no unambiguous meaning. In the weak field limit of GR one has gravitoelectric and gravitomagnetic fields and in general these can be transformed into one another through coordinate transformations that are more general than Lorentz transformations. For example if we have a non-rotating star and a gyroscope in circular orbit around it then in the coordinate system fixed to the asymptotic inertial frame at spatial infinity, the star has a gravitoelectric field that causes the orbiting gyroscope to precess whereas we can perform a coordinate transformation to a system corotating with the gyroscope wherein the gyroscope is at rest, in which case the star acquires a gravitomagnetic field that causes the gyroscope to precess.

In arbitrary curved space-times (not necessarily in the weak field limit) the notion of a gravitoelectric field and that of a gravitomagnetic field are not as transparent. One can however decompose the Riemann curvature tensor into an electric part and a magnetic part (see Bel decomposition) and under infinitesimal Lorentz transformations from one local frame to another at the same event, the electric and magnetic parts will transform into one another in much the same way that the electric and magnetic parts of the electromagnetic field tensor transform under a Lorentz transformation. There is a way to relate the magnetic part of the Riemann tensor to a notion of gravitomagnetism but this is a characterization of the intrinsic gravitomagnetic effects of a space-time such as frame-dragging due to a rotating source; it is not the same thing as describing the geodetic effect using either the gravitoelectric field or the gravitomagnetic field through a coordinate transformation as in the above paragraph.

Now this is all within the framework of GR, including the weak field limit. But it's entirely possible that you're asking about gravitational fields within the framework of SR...are you?

4. Jun 22, 2014

### DrZoidberg

Wow. This stuff goes far over my head. Does it make a big difference whether I look at gravitational fields in the context of SR or GR?

That actually sounds quite similar to what I had in mind when I wrote "gravity transformer".

Something similar to an alcubierre drive?

5. Jun 22, 2014

### pervect

Staff Emeritus
It looks like the paper I'm thinking of is Forward, Robert L, "Guidelines to Antigravity", American Journal of Physics, Volume 31, Issue 3, pp. 166-170 (1963).

It's not like the Alcubierre drive, it's just a way of accelerating a body gravitationally, in such a way that it won't experience any feeling of acceleration.

I'd say that it's mostly of theoretical interest, rather than something that looks practical, in my opinion.