Are there spacetimes or metrics with no global symmetries? Spacetimes/metrics with no global Poincaré, Lorentz, diffeomorphism, CPT, translational and gauge invariances?
And if there are, what does it exactly mean?
For example, I know that in certain expanding spacetimes (like the one representing our universe) the global time translation invariance is broken and therefore energy is not conserved (globally, or at cosmological scales)
If there are spacetimes with no global symmetries, would it mean that all these symmetries would break (or be violated) at global scales?