366 research outputs found
Close limit evolution of Kerr-Schild type initial data for binary black holes
We evolve the binary black hole initial data family proposed by Bishop {\em
et al.} in the limit in which the black holes are close to each other. We
present an exact solution of the linearized initial value problem based on
their proposal and make use of a recently introduced generalized formalism for
studying perturbations of Schwarzschild black holes in arbitrary coordinates to
perform the evolution. We clarify the meaning of the free parameters of the
initial data family through the results for the radiated energy and waveforms
from the black hole collision.Comment: 8 pages, RevTex, four eps figure
Initial data for stationary space-times near space-like infinity
We study Cauchy initial data for asymptotically flat, stationary vacuum
space-times near space-like infinity. The fall-off behavior of the intrinsic
metric and the extrinsic curvature is characterized. We prove that they have an
analytic expansion in powers of a radial coordinate. The coefficients of the
expansion are analytic functions of the angles. This result allow us to fill a
gap in the proof found in the literature of the statement that all
asymptotically flat, vacuum stationary space-times admit an analytic
compactification at null infinity. Stationary initial data are physical
important and highly non-trivial examples of a large class of data with similar
regularity properties at space-like infinity, namely, initial data for which
the metric and the extrinsic curvature have asymptotic expansion in terms of
powers of a radial coordinate. We isolate the property of the stationary data
which is responsible for this kind of expansion.Comment: LaTeX 2e, no figures, 12 page
Conformally flat black hole initial data, with one cylindrical end
We give a complete analytical proof of existence and uniqueness of
extreme-like black hole initial data for Einstein equations, which possess a
cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and
extreme Bowen-York's initial data. This extends and refines a previous result
\cite{dain-gabach09} to a general case of conformally flat, maximal initial
data with angular momentum, linear momentum and matter.Comment: Minor changes and formula (21) revised according to the published
version in Class. Quantum Grav. (2010). Results unchange
Area-charge inequality for black holes
The inequality between area and charge for dynamical black
holes is proved. No symmetry assumption is made and charged matter fields are
included. Extensions of this inequality are also proved for regions in the
spacetime which are not necessarily black hole boundaries.Comment: 21 pages, 2 figure
Initial data for fluid bodies in general relativity
We show that there exist asymptotically flat almost-smooth initial data for
Einstein-perfect fluid's equation that represent an isolated liquid-type body.
By liquid-type body we mean that the fluid energy density has compact support
and takes a strictly positive constant value at its boundary. By almost-smooth
we mean that all initial data fields are smooth everywhere on the initial
hypersurface except at the body boundary, where tangential derivatives of any
order are continuous at that boundary.
PACS: 04.20.Ex, 04.40.Nr, 02.30.JrComment: 38 pages, LaTeX 2e, no figures. Accepted for publication in Phys.
Rev.
Black Hole Interaction Energy
The interaction energy between two black holes at large separation distance
is calculated. The first term in the expansion corresponds to the Newtonian
interaction between the masses. The second term corresponds to the spin-spin
interaction. The calculation is based on the interaction energy defined on the
two black holes initial data. No test particle approximation is used. The
relation between this formula and cosmic censorship is discussed.Comment: 18 pages, 2 figures, LaTeX2
Extreme Bowen-York initial data
The Bowen-York family of spinning black hole initial data depends essentially
on one, positive, free parameter. The extreme limit corresponds to making this
parameter equal to zero. This choice represents a singular limit for the
constraint equations. We prove that in this limit a new solution of the
constraint equations is obtained. These initial data have similar properties to
the extreme Kerr and Reissner-Nordstrom black hole initial data. In particular,
in this limit one of the asymptotic ends changes from asymptotically flat to
cylindrical. The existence proof is constructive, we actually show that a
sequence of Bowen-York data converges to the extreme solution.Comment: 21 page
A new geometric invariant on initial data for Einstein equations
For a given asymptotically flat initial data set for Einstein equations a new
geometric invariant is constructed. This invariant measure the departure of the
data set from the stationary regime, it vanishes if and only if the data is
stationary. In vacuum, it can be interpreted as a measure of the total amount
of radiation contained in the data.Comment: 5 pages. Important corrections regarding the generalization to the
non-time symmetric cas
Asymptotic properties of the development of conformally flat data near spatial infinity
Certain aspects of the behaviour of the gravitational field near null and
spatial infinity for the developments of asymptotically Euclidean, conformally
flat initial data sets are analysed. Ideas and results from two different
approaches are combined: on the one hand the null infinity formalism related to
the asymptotic characteristic initial value problem and on the other the
regular Cauchy initial value problem at spatial infinity which uses Friedrich's
representation of spatial infinity as a cylinder. The decay of the Weyl tensor
for the developments of the class of initial data under consideration is
analysed under some existence and regularity assumptions for the asymptotic
expansions obtained using the cylinder at spatial infinity. Conditions on the
initial data to obtain developments satisfying the Peeling Behaviour are
identified. Further, the decay of the asymptotic shear on null infinity is also
examined as one approaches spatial infinity. This decay is related to the
possibility of selecting the Poincar\'e group out of the BMS group in a
canonical fashion. It is found that for the class of initial data under
consideration, if the development peels, then the asymptotic shear goes to zero
at spatial infinity. Expansions of the Bondi mass are also examined. Finally,
the Newman-Penrose constants of the spacetime are written in terms of initial
data quantities and it is shown that the constants defined at future null
infinity are equal to those at past null infinity.Comment: 24 pages, 1 figur
On the existence of initial data containing isolated black holes
We present a general construction of initial data for Einstein's equations
containing an arbitrary number of black holes, each of which is instantaneously
in equilibrium. Each black hole is taken to be a marginally trapped surface and
plays the role of the inner boundary of the Cauchy surface. The black hole is
taken to be instantaneously isolated if its outgoing null rays are shear-free.
Starting from the choice of a conformal metric and the freely specifiable part
of the extrinsic curvature in the bulk, we give a prescription for choosing the
shape of the inner boundaries and the boundary conditions that must be imposed
there. We show rigorously that with these choices, the resulting non-linear
elliptic system always admits solutions.Comment: 11 pages, 2 figures, RevTeX
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