7 research outputs found
The interior solution of axially symmetric, stationary and rigidly rotating dust configurations
It is shown that the interior solution of axially symmetric, stationary and
rigidly rotating dust configurations is completely determined by the mass
density along the axis of rotation. The particularly interesting case of a mass
density, which is cylindrical symmetric in the interior of the dust
configuration, is presented. Among other things, this proves the non-existence
of homogeneous dust configurations.Comment: minor corrections to the published version, 10 page
Numerical approach for high precision 3-D relativistic star models
A multi-domain spectral method for computing very high precision 3-D stellar
models is presented. The boundary of each domain is chosen in order to coincide
with a physical discontinuity (e.g. the star's surface). In addition, a
regularization procedure is introduced to deal with the infinite derivatives on
the boundary that may appear in the density field when stiff equations of state
are used. Consequently all the physical fields are smooth functions on each
domain and the spectral method is absolutely free of any Gibbs phenomenon,
which yields to a very high precision. The power of this method is demonstrated
by direct comparison with analytical solutions such as MacLaurin spheroids and
Roche ellipsoids. The relative numerical error reveals to be of the order of
. This approach has been developed for the study of relativistic
inspiralling binaries. It may be applied to a wider class of astrophysical
problems such as the study of relativistic rotating stars too.Comment: Minor changes, Phys. Rev. D in pres
Time-Independent Gravitational Fields
This article reviews, from a global point of view, rigorous results on time
independent spacetimes. Throughout attention is confined to isolated bodies at
rest or in uniform rotation in an otherwise empty universe. The discussion
starts from first principles and is, as much as possible, self-contained.Comment: 47 pages, LaTeX, uses Springer cl2emult styl