Multipole Moments in General Relativity

Relation of Cartesian and spherical multipole moments in general relativity

The Earth’s gravitational field is represented by its multipole moments. Multipole moments have two kinds of equivalent forms, that is, the Cartesian symmetric and tracefree tensors and the spherical harmonic coefficients. The relation between these two forms is interesting and useful for some practical problems. Under Newtonian approximation, there exists a simple relation between the aforesai...

Multipole Moments In

This paper contains discussion of the problem of motion of extended e.g. non point test bodies in multidimensional space. Extended bodies are described in terms of so called multipole moments. Using approximated form of equations of motion for extended bodies deviation from geodesic motion is derived. Results are applied to special form of space-time. PACS number(s): 04.25.-g, 04.50.+h, 11.25.Mj

Multipole Moments of Static Spacetimes

Multipole moments of axisymmetric spacetimes

In this thesis we study multipole moments of axisymmetric spacetimes. Using the recursive definition of the multipole moments of Geroch and Hansen we develop a method for computing all multipole moments of a stationary axisymmetric spacetime without the use of a recursion. This is a generalisation of a method developed by Herberthson for the static case. Using Herberthson’s method we also devel...

Aperture Multipole Moments from Weak

The projected mass of a gravitational lens inside (circular) apertures can be derived from the measured shear inside an annulus which is caused by the tidal eld of the deeecting mass distribution. Here we show that also the multipoles of the two-dimensional mass distribution can be derived from the shear in annuli. We derive several expressions for these mass multipole moments in terms of the s...