Do gravity waves imply repulsive force component?

[grokkin]

If you consider empty space case (energy-momentum tensor is zero), the curvature of space is Ricci-flat but the Riemann tensor is not necessarily zero, which allows for gravity waves in empty space. It's not difficult to see that the waves would have to be transverse (analogous to EM waves). What I've been trying to wrap my head around is whether this necessarily implies that there is a repulsive component to the wave. In other words (obvious oversimplification here), if you think of the trough of the wave as regular attractive gravity as we know it, is there a necessary implication that the peak of the wave is repulsive? Thoughts please?

 

[Bill_K]

if you think of the trough of the wave as regular attractive gravity as we know it, is there a necessary implication that the peak of the wave is repulsive?

A gravity wave is quadrupole. Meaning that if a wave passes through a cloud of test particles, the cloud will be sheared (circle -> ellipse and back again) There's no attraction or repulsion associated with the wave.

 

[bcrowell]

It makes sense to define repulsion and attraction in a Newtonian universe where everything happens through instantaneous action at a distance. Once you start talking about fields, it is no longer possible to classify everything as repulsive or attractive. For example, when an electromagnetic wave passes through a region containing a charged particle, it doesn't make sense to ask whether the particle is attracted or repelled.

In GR, the closest thing we have to a meaningful way of saying gravity isn't repulsive is the various energy conditions. E.g., there's the strong energy condition, which is violated by the cosmological constant. Gravitational waves don't violate any energy conditions.

 

[grokkin]

All good points. "Repulsive" was a poor choice of words without further explanation. What I was trying to ask is something like the following:

Consider two particles in otherwise empty space; these two particles experience normal gravitational interaction between themselves. Now consider a gravity wave traveling from far away (i.e. not generated by the system of the two particles) with a wave period of twice the distance between the particles.

What I trying to ask originally is whether such a wave would be experienced by the two particles as an apparent increase in gravitational attraction at the trough and an apparent decrease (and possibly a change of sign, i.e. repulsion) at the peak.

 

[Bill_K]

When you say "attraction", you're talking about the force due to gravity. That's a feature that can be rather elusive in general relativity, since freely falling particles experience no acceleration. Gravitational force and acceleration have meaning only in the linearized theory, where we visualize the gravitational field as a perturbation on a flat background space. In this limited sense you can talk about the Newtonian attraction as a force.

The effect of a passing gravitational wave is to vary the spacetime geometry. In particular the distance between two particles will vary in step with the wave. But this variation is merely superposed on the particle's own motion, not a modification of their attractive force. In fact, the transverse stretching/compressing induced by the wave is proportional: the farther apart the particles are, the greater the effect!

 

[zonde]

Consider two particles in otherwise empty space; these two particles experience normal gravitational interaction between themselves. Now consider a gravity wave traveling from far away (i.e. not generated by the system of the two particles) with a wave period of twice the distance between the particles.

What I trying to ask originally is whether such a wave would be experienced by the two particles as an apparent increase in gravitational attraction at the trough and an apparent decrease (and possibly a change of sign, i.e. repulsion) at the peak.

I believe that the answer is no.
You can read about historical account of arguments around gravitational waves in Wikipedia article Sticky bead argument
According to sticky bead argument single bead is moving on a stick just the same so presence of another bead further away along the stick is not supposed to change the effect of gravitational wave.

 

[Mute]

Just to clarify some terminology:

A "gravity wave" is a kind of wave in (or at the interface of) a fluid system in which the restoring force is gravity or a buoyant force.

A "gravitational wave" is a wave in spacetime.

Although from context here it is clear that "gravitational wave" was meant, it's good to be aware of the separate concepts to avoid ambiguity in other situations. =)

 

[Naty1]

from Bill_K:

The effect of a passing gravitational wave is to vary the spacetime geometry. ...In fact, the transverse stretching/compressing induced by the wave is proportional: the farther apart the particles are, the greater the effect!

yes and in fact this is the basis for detecting gravitational waves via experiemnt...LIGO...One detector is in LA, the other WA state!


http://en.wikipedia.org/wiki/LIGO