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Yes, but what energy is transported here?


Gravitational energy.

Necessary disclaimer: Gravitational energy / energy in General Relativity is notoriously difficult to define and the story of energy conservation is even worse. In general, you can no longer expect energy to be conserved globally. Locally yes, due to the 4-divergence of the energy-momentum tensor vanishing, but globally you can have effects such as cosmic expansion that causes all photons to lose energy as they travel through the universe and, as far as we know, that energy is simply lost.

A few references:

https://en.wikipedia.org/wiki/Conservation_of_energy#General...

https://en.wikipedia.org/wiki/Mass_in_general_relativity




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