KleinMoretti
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- TL;DR Summary
- does the equation βππππ=0. imply conservation of energy
I came across this statement
"The covariant energy-momentum conservation lawis
βππππ=0.
Be careful though: "convariant conservation" equations do not imply that any component of the energy or momentum is actually conserved.
To get actual conserved quantities you need a symmetry. In particular an isometry associated with a Killing vector field."
now when by "convariant conservation" equations do not imply that any component of the energy or momentum is actually conserved." they are talking about global conservation right? because I thought that βππππ=0. did imply energy is conserved locally
"The covariant energy-momentum conservation lawis
βππππ=0.
Be careful though: "convariant conservation" equations do not imply that any component of the energy or momentum is actually conserved.
To get actual conserved quantities you need a symmetry. In particular an isometry associated with a Killing vector field."
now when by "convariant conservation" equations do not imply that any component of the energy or momentum is actually conserved." they are talking about global conservation right? because I thought that βππππ=0. did imply energy is conserved locally