Radiative Gravitational Perturbation Problems in General Relativity: I. Gravitational Radiation from Slowly Rotating Collapse: an Exact Green Function. II. 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. The rotation of the object perturbs this geometry generating gravitational radiation. We derive a Green function relating the radiation received far from the star to boundary conditions on the surface of the star. At late times, we find that this Green function is dominated by a few waves with specific frequencies known as the quasi -normal modes of the Schwarzschild geometry. Post-Post Newtonian Gravitational Radiation from Two-Body Systems. Expanding Einstein's equations in powers of the velocity of the 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. This last set of terms is of lower order than the post-post Newtonian terms that we are examining. The terms independent of the radius of the near zone are the post-post Newtonian radiative terms that we are looking for. Finally, the terms proportional to the radius of the near zone, representing the divergences mentioned above, must be eliminated. This can be accomplished by tuning the gauge--that is by making infinitesimal coordinate changes. The gauge tuning can be done so that those terms independent of the radius of the near zone are not affected, leaving a finite result at post-post Newtonian order.
- Pub Date:
- March 1982
- Physics: Astronomy and Astrophysics