Speaker
Description
Rotating stars with non-uniform deformations are a very important source of continuous gravitational waves, but representing the radiative part of their gravitational field analytically is mostly limited to using the post-Newtonian method (e.g. Blanchet-Damour 1990), which decomposes the zone of the external gravitational field into a ‘near’ (pseudo-stationary) zone and an 'intermediate' (radiative) zone. Such a decomposition is only valid where the rotation rate leads to an emitted wavelength that is longer than the size of the star, and as the rotation rate increases and the emitted wavelength gets shorter, the radiative effects inside the star can no longer be overlooked.
Focusing on the incompressible ellipsoids as this is one of the few examples that can be dealt with analytically, Chandrasekhar (1967) and several others do obtain a representation for the field inside the star, but there is no mention on how to explicitly join it to a suitable vacuum solution as it is not possible to solve for the region outside the tri-axial ellipsoid in closed form if the ellipticity is not small; one typically resorts to ellipsoidal harmonics. To break this impasse we make the assumption that the non-uniform part of the deformation is a small increment on top of the axisymmetric part, which then allows us to demonstrate that all the equations (both interior and exterior) can be explicitly solved in closed form as a boundary value problem. As well as an analytical representation of the radiation over the whole vacuum, this will also allow us to explore radiative behaviour inside the star (e.g. at interfaces).
