System & Environment in Gravity: Is There a Global Theory?

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hi
in classical physics, we can decompose world into system and environment.
is it true in content of gravity?
it seems in general relativity we have a global theory!
 
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The decomposition into system and environment is basically just a completely arbitrary labeling.
 
Thread 'Dirac's integral for the energy-momentum of the gravitational field'

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Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

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