Imagine binary neutron stars inspiral, they generate gravitational wave which carries energy away and causing the pair to become ever closer. Since all wave must carry energy I wonder where do gravitational wave draws their energy from? I know mass is not a conserved quantity so i think it should be the gravitational potential energy converted into kinetic energy but how can vacuum spacetime gains this kinetic energy? Is this perhaps due to moving observer seeing different result compared to nearby observer?
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$\begingroup$ Their momentum is carried away, that's it. Spacetime is as real thing as anything else. $\endgroup$– MithoronCommented Mar 30, 2019 at 1:26
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2 Answers
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In simple terms, if you think of the geometry as a field on a given spacetime, it does not simply consist of a pair of lumps at the position of each neutron star as one would intuitively expect in newtonian dynamics.
Instead, it is a smooth configuration extended to the whole spacetime. Using the ADM formalism, we can actually define a unique energy (ADM energy) corresponding to this geometry configuration.
When the two Neutron Stars get closer, although their "mass" remain constant, the ADM energy of the field is radiated away in the form of GWs. We can say that before the neutron stars collide, Gravitational waves feed directly from the "energy" of the "geometry field" itself.
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$\begingroup$ I mostly like this answer, except that the first sentence of the final paragraph seems to suggest that the ADM energy changes. This is not the case; ADM energy is a property of the entire spacetime — past, present, and future. It is conserved. After the GWs have been emitted, their energy is still included in the ADM energy, because they will always be present on any spacelike slice in the future. $\endgroup$– MikeCommented Apr 17, 2019 at 18:39
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$\begingroup$ Yes, you are right, I guess I meant some localized version of it is traveling with the waves away from the source $\endgroup$ Commented Apr 19, 2019 at 16:25
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Another way to approach the concept is as follows:
The “missing” mass/energy was indeed radiated away as gravitational waves. But that isn't due to mass escaping from a black hole – it comes from the potential energy in the positions and spins of the two black holes.
