Spin and quadrupole contributions to the motion of astrophysical binaries

Compact objects in general relativity approximately move along geodesics of spacetime. It is shown that the corrections to geodesic motion due to spin (dipole), quadrupole, and higher multipoles can be modeled by an extension of the point mass action. The quadrupole contributions are discussed in detail for astrophysical objects like neutron stars or black holes. Implications for binaries are analyzed for a small mass ratio situation. There quadrupole effects can encode information about the internal structure of the compact object, e.g., in principle they allow a distinction between black holes and neutron stars, and also different equations of state for the latter. Furthermore, a connection between the relativistic oscillation modes of the object and a dynamical quadrupole evolution is established.Comment: 43 pages. Proceedings of the 524. WE-Heraeus-Seminar "Equations of Motion in Relativistic Gravity". v2: fixed reference. v3: corrected typos in eqs. (1), (57), (85

Rotating Stars in Relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information one could obtain about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.Comment: 101 pages, 18 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.org