Measuring mass moments and electromagnetic moments of a massive, axisymmetric body, through gravitational waves

The electrovacuum around a rotating massive body with electric charge density is described by its multipole moments (mass moments, mass-current moments, electric moments, and magnetic moments). A small uncharged test particle orbiting around such a body moves on geodesics if gravitational radiation is ignored. The waves emitted by the small body carry information about the geometry of the central object, and hence, in principle, we can infer all its multipole moments. Due to its axisymmetry the source is characterized now by four families of scalar multipole moments: its mass moments $M_l$, its mass-current moments $S_l$, its electrical moments $E_l$ and its magnetic moments $H_l$, where $l=0,1,2,...$. Four measurable quantities, the energy emitted by gravitational waves per logarithmic interval of frequency, the precession of the periastron (assuming almost circular orbits), the precession of the orbital plane (assuming almost equatorial orbits), and the number of cycles emitted per logarithmic interval of frequency, are presented as power series of the newtonian orbital velocity of the test body. The power series coefficients are simple polynomials of the various moments.Comment: Talk given by T. A. A. at Recent Advances in Astronomy and Astrophysics, Lixourion, Kefallinia island, Greece, 8-11 Sep 200

Multipole moments as a tool to infer from gravitational waves the geometry around an axisymmetric body

A binary system, composed of a compact object orbiting around a massive central body, will emit gravitational waves which will depend on the central body's spacetime geometry. We expect that the gravitational wave observables will somehow ``encode'' the information about the spacetime structure. On the other hand, it has been known for some time that the geometry around an axisymmetric body can be described by its (Geroch-Hansen) multipole moments. Therefore one can speculate that using the multipole moments can prove to be a helpful tool for extracting this information. We will try to demonstrate this in this talk, following the procedure described by [F. D. Ryan, Phys. Rev. D {\bf 52} 5707 (1995)] and [T. P. Sotiriou and T. A. Apostolatos, Phys. Rev. D {\bf 71} 044005 (2005)].Comment: Talk given by T. P. S. at Albert Einstein's Century International Conference, Paris, France, 18-22 Jul 200

A weak Hilbert space with few symmetries

We construct a weak Hilbert Banach space such that for every block subspace $Y$ every bounded linear operator on Y is of the form D+S where S is a strictly singular operator and D is a diagonal operator. We show that this yields a weak Hilbert space whose block subspaces are not isomorphic to any of their proper subspaces.Comment: 32 page

Revising the multipole moments of numerical spacetimes, and its consequences

Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the object, and because the construction of a suitable analytic metric that mimics a numerical metric should be based on the multipole moments of the latter one, in order to yield a reliable representation. In this note we show that there has been a widespread delusion in the way the multipole moments of a numerical metric are read from the asymptotic expansion of the metric functions. We show how one should read correctly the first few multipole moments (starting from the quadrupole mass-moment), and how these corrected moments improve the efficiency of describing the metric functions with analytic metrics that have already been used in the literature, as well as other consequences of using the correct moments.Comment: article + supplemental materia