# Which version of the equivalence principle affects the coordinate dependency of the Landau–Lifshitz pseudotensor?

We know that the energy-momentum of gravity can be defined by a pseudotensor called the Landau-Lifshitz pseudotensor, which is coordinate dependent. In fact, the gravitational stress–energy will always vanish locally at any chosen point an inertial frame of reference, because the equivalence principle requires that the gravitational force field vanishes locally in some frames. If gravitational energy is a function of its force field, the associated gravitational pseudotensor must also vanish locally.

Does this hold for the Einstein's equivalence principle (the outcome of any local non-gravitational experiment in a free falling laboratory is independent of the velocity of the laboratory and its location in spacetime)? Or just for the strong equivalence principle?

• It's a mathematical property of the LL pseudotensor - why would it depend on which equivalence principle we adopt? Commented Dec 31, 2023 at 2:27
• More precisely, the LL pseudotensor is built under the assumption that it must be coordinate dependent, see its article in wikipedia Commented Dec 31, 2023 at 3:52
• LL pseudotensor exists only for GR, the theory that satisfies all versions of EPs, so the question does not make sense to me. Commented Dec 31, 2023 at 4:58
• @A.V.S. The question is which equivalence principle makes the LL pseudotensor vanish locally. Commented Dec 31, 2023 at 17:31
• @Manuel it depends which EP you see as requiring GR to be a geometric theory. Once you have a differential geometric framework, local tangent spaces are flat. Commented Jan 2 at 9:40