Einsteinian Gravity


Contracted Curvature <=> Energy-Momentum per unit Volume

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.