What is the difference between sound waves and gravitational waves?

The source term in GR as I understand it is the energy-momentum tensor which contains pressure, which makes me think sound is a subset of gravitational waves. Are there more source terms?

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    $\begingroup$ Any kind of waves produce pressure. EM for example produces radiation pressure which is the main idea behind solar sails. $\endgroup$ Nov 22, 2018 at 17:46

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Sound waves are different from gravitational waves in GR in many ways. Sound waves are disturbances which propagate through some material medium, while gravitational waves are understood as a disturbance in spacetime itself, so they need no such thing. Sound waves also travel at some speed defined by the properties of the medium, and gravitational waves travel at the maximum possible speed, the speed of light.

Pressure in sound waves and in the energy-momentum tensor mean different things. In sound waves, the pressure measures how much the molecules in a piece of the medium are pushing around on it's surroundings. The molecules in a medium are constantly moving and bumping with each other, so that a force at some point in the medium causes a change in pressure that propagates at the speed of sound.

In GR, we have a tensor that measures how much spacetime is curved, and this curvature is determined by the local distribution of mass-energy. The diagonal components are called pressure by analogy with material media, but they measure kinectic energy, which is correlated with pressure in an ideal gas.

Also, to create gravitational waves that aren't immeasurably small, you need really heavy bodies moving really fast. Although Einstein himself predicted their existence in 1916, only recently in 2015 scientists were able to detect them for the first time, by observing the ripples produced by two black holes merging about a billion light years away from us.

  • $\begingroup$ How is pressure in a real gas and an ideal gas different enough to mean different things? Surely one should be able to have real gases in general relativity? $\endgroup$
    – Emil
    Nov 22, 2018 at 18:43
  • $\begingroup$ Ideal gases are just an example of how energy relates to pressure. In a closed system with fixed volume, the pressure of the gas is directly proportional to the (absolute) temperature, and thus directly proportional to the average kinectic energy of its molecules. The expression is just particularly simple in this case. $\endgroup$ Nov 22, 2018 at 18:54
  • $\begingroup$ In general relativity, you can have matter interacting with the metric tensor, but there are also vacuum solutions, where there is no matter at all, and the energy is in the gravitational waves themselves. So that the energy that curves spacetime is due to the curvature of spacetime itself. $\endgroup$ Nov 22, 2018 at 18:58
  • $\begingroup$ Actually, I don't think that is accurate. It's not the energy from the wave that makes vacuum solutions possible, it's that only the stress-energy tensor is not sufficient to describe the evolution of the system, we also need the initial/boundary contitions $\endgroup$ Nov 22, 2018 at 19:14
  • $\begingroup$ To put it simply: The pressure components just mean total kinectic energy, and the actual, mechanical pressure is unimportant. Moving charges are sources for the EM field, analogously, moving masses are sources for the curvature of spacetime. $\endgroup$ Nov 22, 2018 at 19:20

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