I General Relativity: Is it Local?

[accdd]

Spacetime is a differential manifold and at each point is attached a Minkowski spacetime.
There the laws of physics are the usual ones without gravity.
Gravity is the curvature of spacetime. To define the concept of curvature do we need to evaluate at least one neighborhood of point P? Is general relativity local?

 

[vanhees71]

As all so far successful relativistic field theories also GR is local, i.e., it's Lagrangian depends on the fields and its derivatives at a single spacetime point.

 

[Demystifier]

To define the concept of curvature do we need to evaluate at least one neighborhood of point P? Is general relativity local?

An infinitesimally small neighborhood suffices for that purpose, so yes, it's local.