Can conservation laws be deduced from the Einstein field equations?

[Alain De Vos]

Can one deduce from the einstein field equations:
-Conservation of mass
-Conservation of energy
-Conservation of mass-energy
-Conservation of linear momentum
-Conservation of angular momentum
-Principle of least action
?

And does curvature of space-time has a "potential" on certain conditions ?

 

[Matterwave]

You can obtain the Einstein's Field Equation from the principle of least action using the Hilbert Action...

 

[ZealScience]

You can obtain the Einstein's Field Equation from the principle of least action using the Hilbert Action...

Also, principle of least action derives many conservation laws using virtue of symmetries in lagrangian mechanics, if you derive field equation from lagrangians, you atomatically assume that conservation laws are valid.

 

[WannabeNewton]

Otherwise, once you have solved for the metric from the EFEs you can use Killing's Equations to find symmetries/conserved quantities by solving for the respective killing vector fields.

 

[Mentz114]

The Einstein tensor

$$G^{\mu\nu}=R^{\mu\nu}-(1/2)Rg^{\mu\nu}$$

obeys ${G^{\mu\nu}}_{ ;\nu}=\kappa\ {T^{\mu\nu}}_{ ;\nu}=0$ identically as a consequence of satisfying an action prinple. What is conserved is the complex T, the energy-momentum tensor.