990 research outputs found
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 , its
mass-current moments , its electrical moments and its magnetic
moments , where . 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
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
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