332 research outputs found
The Yamabe invariant for axially symmetric two Kerr black holes initial data
An explicit 3-dimensional Riemannian metric is constructed which can be
interpreted as the (conformal) sum of two Kerr black holes with aligned angular
momentum. When the separation distance between them is large we prove that this
metric has positive Ricci scalar and hence positive Yamabe invariant. This
metric can be used to construct axially symmetric initial data for two Kerr
black holes with large angular momentum.Comment: 14 pages, 2 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
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
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
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
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
When is protection from impact needed for the face as well as the eyes in occupational environments?
Background: The most commonly identified reason for requiring or using occupational eye and face protection is for protection against flying objects. Standards vary on what risk may require protection of the eyes alone and what requires protection for the whole face. Information on the minimum energy transfer for face damage to occur is not well-established. Methods: The heads of pigs were used as the common model for human skin. A 6 mm steel ball projected at velocities between 45 and 135 m/s was directed at the face area. Examples of impacts were filmed with a high-speed camera and the resulting damage was rated visually on a scale from 1 (no visible damage) to 5 (penetrated the skin and embedded in the flesh). Results: The results for the cheek area indicate that 85 m/s is the velocity above which damage is more likely to occur unless the skin near the lip is included. For damage to the lip area to be avoided, the velocity needs to be 60 m/s or less. Conclusion: The present data support a maximum impact velocity of 85 m/s, provided the thinner and more vulnerable skin of the lids and orbital adnexa is protected. If the coverage area does not extend to the orbital adnexa, then the absolute upper limit for the velocity is 60 m/s. At this stage, eye-only protection, as represented by the lowest level of impact test in the standards in the form of a drop ball test, is not in question
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
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.
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