Continous symmetry and General Relativity I've read that General Relativity says that there are no global laws for conservation of energy. Does that mean that there is no global continuous symmetry such that the Noether theorem can apply?
 A: There is no continuous symmetry in General Relativity (GR). In general. Yes there are spacetimes that admit symmetries, but in general there are none. 
A symmetry in GR is a Killing vector, with respect to which the metric is invariant, i.e. $L_\psi$g = 0, where $\psi$ is the Killing vector, g the metric, and L is a Lie derivative. There is then a symmetry along the covariant direction of the Killing vector. A coordinate system can then be chosen where one coordinate is along the Killing vector, and the metric is then independent of that coordinate, a symmetry of the spacetime. And the stress energy tensor then gives a conserved quantity. 
As for energy, the only way it is explicitly  and locally and globally conserved in GR is if the spacetime admits a timelike symmetry, symmetry as defined above. Static spacetimes do
There is another way. If the spacetime admits an asymptotic timelike symmetry  at infinity the energy will be globally (i.e., in total, but not in any one local area necessarily) conserved. For instance a black hole can loose mass energy which is radiated away as gravitational waves to infinity. The mass lost equals the total gravitational radiation then - we saw that in the LIGO detections of black holes in 2015. 
The fact that the equations do not change, they are tensorial equations, as you change to any coordinate system does not lead to any conservation law. 
