Radiative gravitational perturbation problems in general relativity: I. Gravitational radiation from slowly rotating collapse: an Exact Green Function. II. Post-Post Newtonian gravitational radiation from two-body systems

Gravitational Radiation from Slowly Rotating Collapse: An Exact Green Function. The production of gravitational radiation by pressureless, axisymmetric, slowly rotating bodies is analyzed within the framework of general relativity. The calculation is carried out through first order in the angular velocity of the rotating body. Through first order, the object remains spherically symmetric, but initially can have an arbitrary internal radial structure. With a spherically symmetric structure, the external geometry is the Schwarzschild geometry. Post-Post Newtonian Gravitational Radiation from Two-Body Systems. Expanding Einstein's equations in powers of the velocity of bodies in a gravitational system, we develop a gravitational radiation formalism involving integrated moments of the matter and field source terms from Einstein's equations. At post-post Newtonian order, we find that certain integrals diverge as we let the boundary of the integration region go to infinity. To avoid divergences, we restrict the integration to the near zone. After doing the integrals over all the source terms, we find that some terms are proportional to the radius of the near zone, some are independent of this radius, and others fall off as the reciprocal of the radius of the near zone