Lorentz or Poincare invariant?

[xiaomaclever]

Generally we say GR is local Lorentz invariant. Does it mean the action or field equation?
Why not Poincare invariant? Thanks!

 

[javierR]

The action (not only in GR but in the standard model) has local Lorentz symmetry, while the field equations, with spacetime tensors for its terms, are covariant (when we write a solution to the field equations, we have to pick a reference frame to write it in, so they must not be *invariant* equations, right?). The Poincare group includes translations, but spacetime does not "look the same" at different points...just from different local Lorentz frames. So no Poincare symmetry. However, a special solution to the field equations does have Poincare invariance: Minkowski.