Dark energy and mass-energy conservation

AmongTheRull
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If dark energy is a property of space-time, and more dark energy is created as space-time increases, and the additional dark energy accelerates the expansion of space-time, what is left of the notion of the conservation of energy or of mass-energy?

Does energy conservation become a purely local property? And if so, how much volume can included in the "location"?
 
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In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
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Thread 'Dirac's integral for the energy-momentum of the gravitational field'

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