derivatives, not covariant derivatives. G is Newton's gravitational constant. Verification Examining the 4 requirement conditions we can see that the first 3 are relatively easy to demonstrate: Since the Einstein tensor, , is itself constructed from the metric, so therefore is Since the Einstein tensor, , is symmetric so is since the additional terms are symmetric by inspection. The Landau–Lifshitz pseudotensor is constructed so that when added to the stress–energy tensor of matter, , its total 4-divergence vanishes: . This follows from the cancellation of the Einstein tensor, , with the stress–energy tensor, by the Einstein field equations; the remaining term vanishes algebraically due to the commutativity of partial derivatives applied across antisymmetric indices. The Landau–Lifshitz pseudotensor appears to include second derivative terms in the metric, but in fact the explicit second derivative terms in the pseudotensor cancel with the implicit second derivative terms contained within the Einstein tensor, . This is more evident when the pseudotensor is directly expressed in terms of the metric tensor or the Levi-Civita connection; only the first derivative terms in the metric survive and these vanish where the frame is locally inertial at any chosen point. As a result, the entire pseudotensor vanishes locally (again, at any chosen point) , which demonstrates the delocalisation of gravitational energy–momentum. Cosmological constant When the Landau–Lifshitz pseudotensor was formulated it was commonly assumed that the cosmological constant, , was zero. Nowadays we don't make that assumption, and the expression needs the addition of a term, giving: This is necessary for consistency with the Einstein field equations. Metric and affine connection versions Landau & Lifshitz also provide two equivalent but longer expressions for the Landau–Lifshitz pseudotensor: Metric tensor version: Affine connection version: This definition of energy–momentum is covariantly applicable not just under Lorentz transformations, but also under general coordinate transformations. Einstein pseudotensor This pseudotensor was originally developed by Albert Einstein. Paul Dirac showed that the mixed Einstein pseudotensor satisfies a conservation law Clearly this pseudotensor for gravitational stress–energy is constructed exclusively from the metric tensor and its first derivatives. Consequently, it vanishes at any event when the coordinate system is chosen to make the first derivatives of the metric vanish because each term in the pseudotensor is quadratic in the first derivatives of the metric. However it is not symmetric, and is therefore not suitable as a basis for defining the angular momentum. See also Bel–Robinson tensor Gravitational wave