# Where is the prediction of the speed of gravity in the EFE?

• I
Gold Member
Newton's law of gravitation cannot be compatible with relativity because the gravity from a massive object applies a force to all other masses infinitely fast. General relativity is supposed to correct this flaw by setting a speed limit on how fast the effect of gravity can reach a distant object. (1) How can one derive the speed of gravity from the EFE? (2) Is this speed c? (3) Is this what is meant by gravitational waves?

phyzguy
(1) This is usually derived by assuming that the metric is a flat-space Minkowski metric plus a small perturbation, and then inserting this into the EFE. See, for example, https://en.wikipedia.org/wiki/Linearized_gravity

(2) Yes

(3) Yes

pervect
Staff Emeritus
Newton's law of gravitation cannot be compatible with relativity because the gravity from a massive object applies a force to all other masses infinitely fast. General relativity is supposed to correct this flaw by setting a speed limit on how fast the effect of gravity can reach a distant object. (1) How can one derive the speed of gravity from the EFE? (2) Is this speed c? (3) Is this what is meant by gravitational waves?

The eletromagnetic anaology to "gravity" is the coulomb force between charges. "Gravity" is similar to the repulsive force between charges. The sign is different for gravity, which always attracts, while charge comes in positive and negative variants and unlike charges attract in electromagnetism. Otherwise there is a lot of simlarity.

Basically, it usually leads to confusion to try to assign a "speed" to the coulomb force. Experimentally, one can't make a charge disappear and see what happens, because charge conservation is built into the laws of electormagnetism, Maxwell's equations.

There is a clear difference between the two. Light from the sun is aberrated by the Earth's orbital motion. Gravitational waves would be predeicted to aberrate in the same manner (if the Sun actually emitted any). Electric and gravitational fields from the sun are not aberrated in the same manner, and assuming that they are leads to wildly innacruate predictions that don't conserve angular momentum, and in the case of gravity would wind up with the Earth spiraling into the sun. For the full technical treatment, see for instance https://arxiv.org/abs/gr-qc/9909087 "Aberration and the Speed of Gravity".

Understanding the gravitational case is much easier if one understands the elctromagnetic case. It becomes clear that when one talks about the "speed of light", one talks about radiation, and not the direction of the coulomb force. The results for gravity are similar even though the details are different.

PeterDonis
Ibix