If I understand this correctly, accelerating charges lose energy in the form of EM waves because they change the electric and magnetic fields, which "costs" energy. Does that mean that accelerating masses lose energy too, because they change the gravitational field (i.e. curve spacetime)?
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$\begingroup$ Yes. Gravity waves. en.wikipedia.org/wiki/Gravitational_wave $\endgroup$– Brandon EnrightCommented Aug 16, 2014 at 19:10
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$\begingroup$ It's not really acceleration $d^2x/dt^2$ that matters, it's $d^3x/dt^3$. A simple example is two sheets of mass falling toward one another; they give zero radiation. Another way of putting it is that you need an oscillating mass quadrupole. (You can't have a mass dipole.) $\endgroup$– user4552Commented Aug 17, 2014 at 0:13
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Yes, it an extremely small effect but it exists in Einsteins general relativity. There is one case of a double star where there rotation around each other seems to lose energy at rate that this phenomena should give according to general relativity
