Assumptions:

• The spacetime of experience [at the macroscopic level] is well-characterized as a smooth four-dimensional manifold with a metric and a connection compatible with that metric.
  
• The metric is locally Minkowskian, so that for nearby points in spacetime we recover the effects of Special Relativity.
  
• The effects of a permanent gravitational field are encoded in the Curvature of spacetime and are discernable by the relative acceleration of observers moving along geodesic paths in the existing spacetime.
  
• The motion of test particles [one's with negligible mass-energy] is given by the geodesic paths in the spacetime
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• This geometrical structure is not static; the local curvature is affected by the distribution of matter at that point. The matter-geometry connection constitutes one of the central tenants of the theory and it relates some aspects of curvature to some aspects of material phenomena:

The Einstein program: Given the descriptors for the energy and momentum content of the physical system one wishes to characterize, then

1. Solve the 10 nonlinear partial differential equations for the components of the metric that satisfy the Einstein field equations
   
2. Use the solution's metric components to calculate the full curvature and, as a result, characterize the gravitational field throughout the spacetime manifold.
   
3. Use the solution's metric compatible connection to determine the motion of test particles, including the motion of light rays.