645 research outputs found
Falloff of the Weyl scalars in binary black hole spacetimes
The peeling theorem of general relativity predicts that the Weyl curvature
scalars Psi_n (n=0...4), when constructed from a suitable null tetrad in an
asymptotically flat spacetime, fall off asymptotically as r^(n-5) along
outgoing radial null geodesics. This leads to the interpretation of Psi_4 as
outgoing gravitational radiation at large distances from the source. We have
performed numerical simulations in full general relativity of a binary black
hole inspiral and merger, and have computed the Weyl scalars in the standard
tetrad used in numerical relativity. In contrast with previous results, we
observe that all the Weyl scalars fall off according to the predictions of the
theorem.Comment: 7 pages, 3 figures, published versio
Operational significance of the deviation equation in relativistic geodesy
Deviation equation: Second order differential equation for the 4-vector which
measures the distance between reference points on neighboring world lines in
spacetime manifolds.
Relativistic geodesy: Science representing the Earth (or any planet),
including the measurement of its gravitational field, in a four-dimensional
curved spacetime using differential-geometric methods in the framework of
Einstein's theory of gravitation (General Relativity).Comment: 9 pages, 4 figures, contribution to the "Encyclopedia of Geodesy".
arXiv admin note: text overlap with arXiv:1811.1047
Some notes on the Kruskal - Szekeres completion
The Kruskal - Szekeres (KS) completion of the Schwarzschild spacetime is open
to Synge's methodological criticism that the KS procedure generates "good"
coordinates from "bad". This is addressed here in two ways: First I generate
the KS coordinates from Israel coordinates, which are also "good", and then I
generate the KS coordinates directly from a streamlined integration of the
Einstein equations.Comment: One typo correcte
Explicit Global Coordinates for Schwarzschild and Reissner-Nordstroem
We construct coordinate systems that cover all of the Reissner-Nordstroem
solution with m>|q| and m=|q|, respectively. This is possible by means of
elementary analytical functions. The limit of vanishing charge q provides an
alternative to Kruskal which, to our mind, is more explicit and simpler. The
main tool for finding these global charts is the description of highly
symmetrical metrics by two-dimensional actions. Careful gauge fixing yields
global representatives of the two-dimensional theory that can be rewritten
easily as the corresponding four-dimensional line elements.Comment: 12 pages, 3 Postscript figures, sign error in Eq. (37) and below
corrected, references and Note added; to appear in Class. Quantum Gra
A Radiation Scalar for Numerical Relativity
This letter describes a scalar curvature invariant for general relativity
with a certain, distinctive feature. While many such invariants exist, this one
vanishes in regions of space-time which can be said unambiguously to contain no
gravitational radiation. In more general regions which incontrovertibly support
non-trivial radiation fields, it can be used to extract local,
coordinate-independent information partially characterizing that radiation.
While a clear, physical interpretation is possible only in such radiation
zones, a simple algorithm can be given to extend the definition smoothly to
generic regions of space-time.Comment: 4 pages, 1 EPS figur
No-Go Theorem in Spacetimes with Two Commuting Spacelike Killing Vectors
Four-dimensional Riemannian spacetimes with two commuting spacelike Killing
vectors are studied in Einstein's theory of gravity, and found that no outer
apparent horizons exist, provided that the dominant energy condition holds.Comment: latex, 1 figure, version published in Gen. Relativ. Grav., 37,
1919-1926 (2005
Moderate deviations for the determinant of Wigner matrices
We establish a moderate deviations principle (MDP) for the log-determinant
of a Wigner matrix matching four moments with
either the GUE or GOE ensemble. Further we establish Cram\'er--type moderate
deviations and Berry-Esseen bounds for the log-determinant for the GUE and GOE
ensembles as well as for non-symmetric and non-Hermitian Gaussian random
matrices (Ginibre ensembles), respectively.Comment: 20 pages, one missing reference added; Limit Theorems in Probability,
Statistics and Number Theory, Springer Proceedings in Mathematics and
Statistics, 201
Transverse frames for Petrov type I spacetimes: a general algebraic procedure
We develop an algebraic procedure to rotate a general Newman-Penrose tetrad
in a Petrov type I spacetime into a frame with Weyl scalars and
equal to zero, assuming that initially all the Weyl scalars are non
vanishing. The new frame highlights the physical properties of the spacetime.
In particular, in a Petrov Type I spacetime, setting and
to zero makes apparent the superposition of a Coulomb-type effect
with transverse degrees of freedom and .Comment: 10 pages, submitted to Classical Quantum Gravit
An explanation of the Newman-Janis Algorithm
After the original discovery of the Kerr metric, Newman and Janis showed that
this solution could be ``derived'' by making an elementary complex
transformation to the Schwarzschild solution. The same method was then used to
obtain a new stationary axisymmetric solution to Einstein's field equations now
known as the Kerr-newman metric, representing a rotating massive charged black
hole. However no clear reason has ever been given as to why the Newman-Janis
algorithm works, many physicist considering it to be an ad hoc procedure or
``fluke'' and not worthy of further investigation. Contrary to this belief this
paper shows why the Newman-Janis algorithm is successful in obtaining the
Kerr-Newman metric by removing some of the ambiguities present in the original
derivation. Finally we show that the only perfect fluid generated by the
Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov
typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra
A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime
We describe a simple family of analytical coordinate systems for the
Schwarzschild spacetime. The coordinates penetrate the horizon smoothly and are
spatially isotropic. Spatial slices of constant coordinate time feature a
trumpet geometry with an asymptotically cylindrical end inside the horizon at a
prescribed areal radius (with ) that serves as the free
parameter for the family. The slices also have an asymptotically flat end at
spatial infinity. In the limit the spatial slices lose their trumpet
geometry and become flat -- in this limit, our coordinates reduce to
Painlev\'e-Gullstrand coordinates.Comment: 7 pages, 3 figure
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