Kinematics and dynamics of general relativity

Spacetime is treated from the point of view of the Cauchy problem. According to this approach a classical gravitational field is the time history of the geometry of a spacelike hypersurface. In order to construct a gravitational field it is necessary to solve the initial-value problem, prescribe a reference system, and integrate the dynamical equations along the trajectories of the reference system. Initial-value and evolution equations or equations of state of any external sources must also be taken into account. The carrying out of this program requires the introduction of a space-plus-time (3 plus 1) formalism. Emphasis in this treatment is on the geometry of the general problem as a guide to methods of calculation.