# Would a graviton follow the geodesic?

Gold Member

## Main Question or Discussion Point

A graviton, if massless, is generally expected to travel at c. If so, we would not expect it to follow the geodesic, which is the path a hypothetical particle with infinite speed. Therefore I would think for example that a massless graviton that was gravitationally lensed around a galaxy would curve about twice as much as the Newtonian prediction for a particle of speed c (1x curvature due to the geodesic and another 1x due to the fact that the speed is c instead of infinite).

Would this mean that a graviton cannot escape from inside a Schwarzschild radius (except for very rare quantum tunneling), or are gravitons hypothesized to follow different rules from photons?

Chalnoth
If so, we would not expect it to follow the geodesic, which is the path a hypothetical particle with infinite speed.
Er, that's not what a geodesic is. A geodesic is the shortest space-time path between two points, and it takes the mass of the particle into account.

Therefore I would think for example that a massless graviton that was gravitationally lensed around a galaxy would curve about twice as much as the Newtonian prediction for a particle of speed c (1x curvature due to the geodesic and another 1x due to the fact that the speed is c instead of infinite).
Well, it is true that the gravitational lensing in GR is twice that in Newtonian gravity, but this is because GR responds to both the pressure and the energy, not because of the difference in speed (you assume photons move at the speed of light to estimate what Newtonian gravity would predict for lensing, and get a number half the GR prediction...the exact same reasoning would work for gravitons).

Would this mean that a graviton cannot escape from inside a Schwarzschild radius (except for very rare quantum tunneling), or are gravitons hypothesized to follow different rules from photons?
Yes, gravitons can't escape the interior of black holes, though I don't think that quantum tunneling gets them out either.

Gold Member
My bad (for using the wrong definition for geodesic). What is correct then is that the graviton should follow the geodesic for a small speed-of-light particle (assuming that's the speed of a graviton). If the center of mass of a black hole accelerates, I think that in itself would create a gravitational wave composed of gravitons which carry energy. If so, do the gravitons originate from outside the Schwarzschild radius? They can't directly travel from inside.

Also the speculation that gravitons may be able to "tunnel out" or spontaneously carry energy away from the vicinity of the black hole (something like Hawking radiation of photons) would probably not be a very significant effect, even if it did happen. I only mentioned it to distinguish it from the more significant source of gravitons.

Chalnoth
My bad (for using the wrong definition for geodesic). What is correct then is that the graviton should follow the geodesic for a small speed-of-light particle (assuming that's the speed of a graviton). If the center of mass of a black hole accelerates, I think that in itself would create a gravitational wave composed of gravitons which carry energy. If so, do the gravitons originate from outside the Schwarzschild radius? They can't directly travel from inside.

Also the speculation that gravitons may be able to "tunnel out" or spontaneously carry energy away from the vicinity of the black hole (something like Hawking radiation of photons) would probably not be a very significant effect, even if it did happen. I only mentioned it to distinguish it from the more significant source of gravitons.
Well, bear in mind that a stable black hole isn't a source of gravitational radiation.

Gold Member
Would the motion of two (otherwise stable) black holes orbiting each other be a source of gravitational waves? If so, would the gravitons therefore have to originate from outside the black holes?

Keep in mind that the Coulomb force between two static charges is not mediated by real, but vertual photons. It should be expected that Coulombic gravitational forces would not be mediated by real, but vertual gravitons.

Chalnoth
Keep in mind that the Coulomb force between two static charges is not mediated by real, but vertual photons. It should be expected that Coulombic gravitational forces would not be mediated by real, but vertual gravitons.
Well, virtual particles become real particles in the limit of large interaction distances. There's no hard and fast distinction between the two.

Chalnoth
Would the motion of two (otherwise stable) black holes orbiting each other be a source of gravitational waves? If so, would the gravitons therefore have to originate from outside the black holes?
Well, it's not quite so simple.

Yes, two black holes orbiting one another emit gravitational radiation. That gravitational radiation comes from the time-dependent nature of the gravitational field (it's not quite that simple: you need more than simple time dependence, but that's the heart of it). Basically, when you have a gravitational field that changes in time in a certain manner, it sets up oscillations in space-time that propagate out from the system in question.

Now, the precise manner in which this relates to the behavior of gravitons, and how gravitons relate to black holes, I am not certain. I think we would need to have a quantum theory of gravity to say that, and even then I'm not sure there would be a simple, intuitive explanation (though obviously the mathematics must work out).

Well, virtual particles become real particles in the limit of large interaction distances. There's no hard and fast distinction between the two.
We won't see any real photons involved in the Coulomb force between two static charges. By inference, rather than any solid theory, real gravitons would not be present where one does not have gravity waves.

Well, virtual particles become real particles in the limit of large interaction distances. There's no hard and fast distinction between the two.
We won't see any real photons involved in the Coulomb force between two static charges. By inference, rather than any solid theory, real gravitons would not be present where one does not have gravity waves.

It is not real photons that communicate the charge within a black hole, nor by inference would real gravitons communicate the mass within the event horizon.