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Post-Newtonian Theory

The post-Newtonian (pN) gravitational theory is the dynamical theory of the slow-motion and weak-field regime of the Einstein theory of gravity. Its validity is restricted to velocities of matter smaller than about one half of the speed of light, c, and to gravitational potentials smaller than about one third of c^2. The pN theory is a perturbative scheme which is constructed as power series in 1/c, more precisely, as expansions in terms of (log c)^l/c^m. Terms containing `logs' are typical for tail contributions, i.e. contributions where backscattering off the gravitational field is involved. Those terms do not enter the formalism before the 4pN level, where `npN' means order (1/c^2)^n beyond leading order.

The importance of the pN theory can be seen in the richness of explicit analytical expressions it delivers, as well as in its close relationship to the well-understood Newtonian theory of gravity.

The European Network aims at developping the pN theory in several directions and applying it to various areas, above all, to provide better physical understanding and confirmation of numerical simulations. This includes:

  1. reformulation of the first post-Newtonian analytical gravitational wave form expressions, useful for numerical calculations,
  2. derivation of the first post-Newtonian radiation damping in a form optimally useful for numerics,
  3. numerical implementation of the above as module in Cactus, including advanced equations of state, to study the collapse of rotating evolved stellar cores, and initial stages of merging neutron star binaries,
  4. reformulation of the fully relativistic initial value problem to account for post-Newtonian physics input (better Cactus module).

This work has been supported by the EU Programme 'Improving the Human Research Potential and the Socio-Economic Knowledge Base' (Research Training Network Contract HPRN-CT-2000-00137).