8 research outputs found
On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system
In a previous work \cite{An1} matter models such that the energy density
and the radial- and tangential pressures and
satisfy were considered in the context of
Buchdahl's inequality. It was proved that static shell solutions of the
spherically symmetric Einstein equations obey a Buchdahl type inequality
whenever the support of the shell, satisfies
Moreover, given a sequence of solutions such that then the
limit supremum of was shown to be bounded by
In this paper we show that the hypothesis
that can be realized for Vlasov matter, by constructing a
sequence of static shells of the spherically symmetric Einstein-Vlasov system
with this property. We also prove that for this sequence not only the limit
supremum of is bounded, but that the limit is
since for Vlasov matter.
Thus, static shells of Vlasov matter can have arbitrary close to
which is interesting in view of \cite{AR2}, where numerical evidence is
presented that 8/9 is an upper bound of of any static solution of the
spherically symmetric Einstein-Vlasov system.Comment: 20 pages, Late
Corotating and irrotational binary black holes in quasi-circular orbits
A complete formalism for constructing initial data representing black-hole
binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in
general, true equilibrium binary configurations. However, when the timescale
for orbital decay is much longer than the orbital period, a binary can be
considered to be in quasi-equilibrium. If each black hole is assumed to be in
quasi-equilibrium, then a complete set of boundary conditions for all initial
data variables can be developed. These boundary conditions are applied on the
apparent horizon of each black hole, and in fact force a specified surface to
be an apparent horizon. A global assumption of quasi-equilibrium is also used
to fix some of the freely specifiable pieces of the initial data and to
uniquely fix the asymptotic boundary conditions. This formalism should allow
for the construction of completely general quasi-equilibrium black hole binary
initial data.Comment: 13 pages, no figures, revtex4; Content changed slightly to reflect
fact that regularized shift solutions do satisfy the isometry boundary
condition
Nonlocal Equation of State in Anisotropic Static Fluid Spheres in General Relativity
We show that it is possible to obtain credible static anisotropic spherically
symmetric matter configurations starting from known density profiles and
satisfying a nonlocal equation of state. These particular types of equation of
state describe, at a given point, the components of the corresponding
energy-momentum tensor not only as a function at that point, but as a
functional throughout the enclosed configuration. To establish the physical
plausibility of the proposed family of solutions satisfying nonlocal equation
of state, we study the constraints imposed by the junction and energy
conditions on these bounded matter distributions.
We also show that it is possible to obtain physically plausible static
anisotropic spherically symmetric matter configurations, having nonlocal
equations of state\textit{,}concerning the particular cases where the radial
pressure vanishes and, other where the tangential pressures vanishes. The later
very particular type of relativistic sphere with vanishing tangential stresses
is inspired by some of the models proposed to describe extremely magnetized
neutron stars (magnetars) during the transverse quantum collapse.Comment: 21 pages, 1 figure, minor changes in the text, references added, two
new solutions studie
Comparing initial-data sets for binary black holes
We compare the results of constructing binary black hole initial data with
three different decompositions of the constraint equations of general
relativity. For each decomposition we compute the initial data using a
superposition of two Kerr-Schild black holes to fix the freely specifiable
data. We find that these initial-data sets differ significantly, with the ADM
energy varying by as much as 5% of the total mass. We find that all
initial-data sets currently used for evolutions might contain unphysical
gravitational radiation of the order of several percent of the total mass. This
is comparable to the amount of gravitational-wave energy observed during the
evolved collision. More astrophysically realistic initial data will require
more careful choices of the freely specifiable data and boundary conditions for
both the metric and extrinsic curvature. However, we find that the choice of
extrinsic curvature affects the resulting data sets more strongly than the
choice of conformal metric.Comment: 18 pages, 12 figures, accepted for publication in Phys. Rev.
Circular orbits of corotating binary black holes: comparison between analytical and numerical results
We compare recent numerical results, obtained within a ``helical Killing
vector'' (HKV) approach, on circular orbits of corotating binary black holes to
the analytical predictions made by the effective one body (EOB) method (which
has been recently extended to the case of spinning bodies). On the scale of the
differences between the results obtained by different numerical methods, we
find good agreement between numerical data and analytical predictions for
several invariant functions describing the dynamical properties of circular
orbits. This agreement is robust against the post-Newtonian accuracy used for
the analytical estimates, as well as under choices of resummation method for
the EOB ``effective potential'', and gets better as one uses a higher
post-Newtonian accuracy. These findings open the way to a significant
``merging'' of analytical and numerical methods, i.e. to matching an EOB-based
analytical description of the (early and late) inspiral, up to the beginning of
the plunge, to a numerical description of the plunge and merger. We illustrate
also the ``flexibility'' of the EOB approach, i.e. the possibility of
determining some ``best fit'' values for the analytical parameters by
comparison with numerical data.Comment: Minor revisions, accepted for publication in Phys. Rev. D, 19 pages,
6 figure
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