On the difference between Poincar\'e and Lorentz gravity

Understand

The Poincar\'e invariance of GR is usually interpreted as Lorentz invariance plus diffeomorphism invariance.

• In this paper, by introducing the local inertial coordinates (LIC), it is shown that a theory with Lorentz and diffeomorphism invariance is not necessarily Poincar\'e invariant.
• Actually, the energy-momentum conservation is violated there.
• On the other hand, with the help of the LIC, the Poincar\'e invariance is reinterpreted as an internal symmetry.