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I was reading this paper that puts forward the argument that Gravitational energy in GR is unnecessary and doesn't exist and that got me wondering if this is a fringe theory or what exactly is the mainstream view regarding the existence of gravitational energy in GR?(i know about the localization problem, i mean beyond that)

Is GR formulated under the assumption that gravitational energy exists?

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It depends.

As you mentioned, there is no stress tensor for the gravitational field. Hence, we can't localize gravitational energy. In this specific sense, it is common to say there is no gravitational energy. I should add that you can define pseudotensors.

Globally, however, you can define notions of energy that comprise both matter and gravitational contributions. There are a few different notions that may or not coincide depending on the specific problem you're interested in (for example, some of them might change with time, while others are conserved). They are the Komar mass the ADM mass, and the Bondi–Sachs mass. At least some of these definitions require asymptotically flat or stationary spacetimes and they are all discussed in Wikipedia. I am unaware of any definition that encompasses all spacetimes (and that would likely be meaningless anyway, since a constant cosmological constant would be expected to lead to a diverging energy in a spacetime that is not spatially compact).

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  • $\begingroup$ "In this specific sense, it is common to say there is no gravitational energy." yes i know about the localisation problem, but the paper i linked was not talking about this kind of "non-existence" of the gravitational energy, they argue it doesnt exist at all- as a consequence they say gravitational waves cant carry energy- and this belief is what im wondering if its considered mainstream or not $\endgroup$
    – FACald
    Commented May 21 at 22:29
  • $\begingroup$ @FACald GWs can accelerate test particles, and gravitons can lead to pair creation in the quantum theory. They surely can carry energy (but not in a stress tensor sense) $\endgroup$ Commented May 21 at 22:59

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