124 research outputs found
Painleve-Gullstrand Coordinates for the Kerr Solution
We construct a coordinate system for the Kerr solution, based on the zero
angular momentum observers dropped from infinity, which generalizes the
Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr
metric can then be interpreted as describing space flowing on a (curved)
Riemannian 3-manifold. The stationary limit arises as the set of points on this
manifold where the speed of the flow equals the speed of light, and the
horizons as the set of points where the radial speed equals the speed of light.
A deeper analysis of what is meant by the flow of space reveals that the
acceleration of free-falling objects is generally not in the direction of this
flow. Finally, we compare the new coordinate system with the closely related
Doran coordinate system.Comment: 6 pages; v2: new section, matches final published version; v3: sign
error in the expression of the function delta correcte
Tetrads in SU(3) X SU(2) X U(1) Yang-Mills geometrodynamics
The relationship between gauge and gravity amounts to understanding
underlying new geometrical local structures. These structures are new tetrads
specially devised for Yang-Mills theories, Abelian and Non-Abelian in
four-dimensional Lorentzian spacetimes. In the present manuscript a new tetrad
is introduced for the Yang-Mills SU(3) X SU(2) X U(1) formulation. These new
tetrads establish a link between local groups of gauge transformations and
local groups of spacetime transformations. New theorems are proved regarding
isomorphisms between local internal SU(3) X SU(2) X U(1) groups and local
tensor products of spacetime LB1 and LB2 groups of transformations. The new
tetrads and the stress-energy tensor allow for the introduction of three new
local gauge invariant objects. Using these new gauge invariant objects and in
addition a new general local duality transformation, a new algorithm for the
gauge invariant diagonalization of the Yang-Mills stress-energy tensor is
developed.Comment: There is a new appendix. The unitary transformations by local SU(2)
subgroup elements of a local group coset representative is proved to be a new
local group coset representative. This proof is relevant to the study of the
memory of the local tetrad SU(3) generated gauge transformations. Therefore,
it is also relevant to the group theorems proved in the paper. arXiv admin
note: substantial text overlap with arXiv:gr-qc/060204
Asymptotic expansions of the Cotton-York tensor on slices of stationary spacetimes
We discuss expansions for the Cotton-York tensor near infinity for arbitrary
slices of stationary spacetimes. From these expansions it follows directly that
a necessary condition for the existence of conformally flat slices in
stationary solutions is the vanishing of a certain quantity of quadrupolar
nature (obstruction). The obstruction is nonzero for the Kerr solution. Thus,
the Kerr metric admits no conformally flat slices. An analysis of higher orders
in the expansions of the Cotton-York tensor for solutions such that the
obstruction vanishes suggests that the only stationary solution admitting
conformally flat slices are the Schwarzschild family of solutions.Comment: Revised version to appear in Class. Quantum Grav. with 13 pages.
Section 2 regarding multipolar expansions of stationary spacetimes largely
expanded. A Maple script demonstrating the calculations in the axially
symmetric case is available upon request from the autho
Quasi-circular Orbits for Spinning Binary Black Holes
Using an effective potential method we examine binary black holes where the
individual holes carry spin. We trace out sequences of quasi-circular orbits
and locate the innermost stable circular orbit as a function of spin. At large
separations, the sequences of quasi-circular orbits match well with
post-Newtonian expansions, although a clear signature of the simplifying
assumption of conformal flatness is seen. The position of the ISCO is found to
be strongly dependent on the magnitude of the spin on each black hole. At close
separations of the holes, the effective potential method breaks down. In all
cases where an ISCO could be determined, we found that an apparent horizon
encompassing both holes forms for separations well inside the ISCO.
Nevertheless, we argue that the formation of a common horizon is still
associated with the breakdown of the effective potential method.Comment: 13 pages, 10 figures, submitted to PR
Time asymmetric spacetimes near null and spatial infinity. I. Expansions of developments of conformally flat data
The Conformal Einstein equations and the representation of spatial infinity
as a cylinder introduced by Friedrich are used to analyse the behaviour of the
gravitational field near null and spatial infinity for the development of data
which are asymptotically Euclidean, conformally flat and time asymmetric. Our
analysis allows for initial data whose second fundamental form is more general
than the one given by the standard Bowen-York Ansatz. The Conformal Einstein
equations imply upon evaluation on the cylinder at spatial infinity a hierarchy
of transport equations which can be used to calculate in a recursive way
asymptotic expansions for the gravitational field. It is found that the the
solutions to these transport equations develop logarithmic divergences at
certain critical sets where null infinity meets spatial infinity. Associated to
these, there is a series of quantities expressible in terms of the initial data
(obstructions), which if zero, preclude the appearance of some of the
logarithmic divergences. The obstructions are, in general, time asymmetric.
That is, the obstructions at the intersection of future null infinity with
spatial infinity are different, and do not generically imply those obtained at
the intersection of past null infinity with spatial infinity. The latter allows
for the possibility of having spacetimes where future and past null infinity
have different degrees of smoothness. Finally, it is shown that if both sets of
obstructions vanish up to a certain order, then the initial data has to be
asymptotically Schwarzschildean to some degree.Comment: 32 pages. First part of a series of 2 papers. Typos correcte
Further insights into the role of T222P variant of RXFP2 in non-syndromic cryptorchidism in two Mediterranean populations
Can Schwarzschildean gravitational fields suppress gravitational waves?
Gravitational waves in the linear approximation propagate in the
Schwarzschild spacetime similarly as electromagnetic waves. A fraction of the
radiation scatters off the curvature of the geometry. The energy of the
backscattered part of an initially outgoing pulse of the quadrupole
gravitational radiation is estimated by compact formulas depending on the
initial energy, the Schwarzschild radius, and the location and width of the
pulse. The backscatter becomes negligible in the short wavelength regime.Comment: 18 pages, Revtex. Added three references; a new comment in Sec. 7;
several misprints corrected. To appear in the Phys. Rev.
Initial data for two Kerr-like black holes
We prove the existence of a family of initial data for the Einstein vacuum
equation which can be interpreted as the data for two Kerr-like black holes in
arbitrary location and with spin in arbitrary direction. When the mass
parameter of one of them is zero, this family reduces exactly to the Kerr
initial data. The existence proof is based on a general property of the Kerr
metric which can be used in other constructions as well. Further
generalizations are also discussed.Comment: revtex, 5 pages, no figure
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.
Binary black holes in circular orbits. II. Numerical methods and first results
We present the first results from a new method for computing spacetimes
representing corotating binary black holes in circular orbits. The method is
based on the assumption of exact equilibrium. It uses the standard 3+1
decomposition of Einstein equations and conformal flatness approximation for
the 3-metric. Contrary to previous numerical approaches to this problem, we do
not solve only the constraint equations but rather a set of five equations for
the lapse function, the conformal factor and the shift vector. The orbital
velocity is unambiguously determined by imposing that, at infinity, the metric
behaves like the Schwarzschild one, a requirement which is equivalent to the
virial theorem. The numerical scheme has been implemented using multi-domain
spectral methods and passed numerous tests. A sequence of corotating black
holes of equal mass is calculated. Defining the sequence by requiring that the
ADM mass decrease is equal to the angular momentum decrease multiplied by the
orbital angular velocity, it is found that the area of the apparent horizons is
constant along the sequence. We also find a turning point in the ADM mass and
angular momentum curves, which may be interpreted as an innermost stable
circular orbit (ISCO). The values of the global quantities at the ISCO,
especially the orbital velocity, are in much better agreement with those from
third post-Newtonian calculations than with those resulting from previous
numerical approaches.Comment: 27 pages, 20 PostScript figures, improved presentation of the
regularization procedure for the shift vector, new section devoted to the
check of the momentum constraint, references added + minor corrections,
accepted for publication in Phys. Rev.
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