6,275 research outputs found
Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing
We use the canonical formalism developed together with David Robinson to st=
udy the Einstein equations on a null surface. Coordinate and gauge conditions =
are introduced to fix the triad and the coordinates on the null surface. Toget=
her with the previously found constraints, these form a sufficient number of
second class constraints so that the phase space is reduced to one pair of
canonically conjugate variables: \Ac_2\and\Sc^2. The formalism is related to
both the Bondi-Sachs and the Newman-Penrose methods of studying the
gravitational field at null infinity. Asymptotic solutions in the vicinity of
null infinity which exclude logarithmic behavior require the connection to fall
off like after the Minkowski limit. This, of course, gives the previous
results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off
more slowly leads to logarithmic behavior which leaves null infinity intact,
allows for meaningful gravitational radiation, but the peeling theorem does not
extend to in the terminology of Newman-Penrose. The conclusions are in
agreement with those of Chrusciel, MacCallum, and Singleton. This work was
begun as a preliminary study of a reduced phase space for quantization of
general relativity.Comment: magnification set; pagination improved; 20 pages, plain te
Spin and Center of Mass in Axially Symmetric Einstein-Maxwell Spacetimes
We give a definition and derive the equations of motion for the center of
mass and angular momentum of an axially symmetric, isolated system that emits
gravitational and electromagnetic radiation. A central feature of this
formulation is the use of Newman-Unti cuts at null infinity that are generated
by worldlines of the spacetime. We analyze some consequences of the results and
comment on the generalization of this work to general asymptotically flat
spacetimes.Comment: 20 page
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
Finding Principal Null Direction for Numerical Relativists
We present a new method for finding principal null directions (PNDs). Because
our method assumes as input the intrinsic metric and extrinsic curvature of a
spacelike hypersurface, it should be particularly useful to numerical
relativists. We illustrate our method by finding the PNDs of the
Kastor-Traschen spacetimes, which contain arbitrarily many black holes in
a de Sitter back-ground.Comment: 10 pages, LaTeX style, WU-AP/38/93. Figures are available (hard
copies) upon requests [[email protected] (H.Shinkai)
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations
This is the first in a series of articles on the numerical solution of
Friedrich's conformal field equations for Einstein's theory of gravity. We will
discuss in this paper why one should be interested in applying the conformal
method to physical problems and why there is good hope that this might even be
a good idea from the numerical point of view. We describe in detail the
derivation of the conformal field equations in the spinor formalism which we
use for the implementation of the equations, and present all the equations as a
reference for future work. Finally, we discuss the implications of the
assumptions of a continuous symmetry.Comment: 19 pages, LaTeX2
Integration of the Friedmann equation for universes of arbitrary complexity
An explicit and complete set of constants of the motion are constructed
algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models
consisting of an arbitrary number of non-interacting species. The inheritance
of constants of the motion from simpler models as more species are added is
stressed. It is then argued that all FLRW models admit what amounts to a unique
candidate for a gravitational epoch function (a dimensionless scalar invariant
derivable from the Riemann tensor without differentiation which is monotone
throughout the evolution of the universe). The same relations that lead to the
construction of constants of the motion allow an explicit evaluation of this
function. In the simplest of all models, the CDM model, it is shown
that the epoch function exists for all models with , but for
almost no models with .Comment: Final form to appear in Physical Review D1
Gravitational Wave Emission from a Bounded Source: the Nonlinear Regime
We study the dynamics of a bounded gravitational collapsing configuration
emitting gravitational waves, where the exterior spacetime is described by
Robinson-Trautman geometries. The full nonlinear regime is examined by using
the Galerkin method that allows us to reduce the equations governing the
dynamics to a finite-dimensional dynamical system, after a proper truncation
procedure. Amongst the obtained results of the nonlinear evolution, one of the
most impressive is the fact that the distribution of the mass fraction
extracted by gravitational wave emission satisfies the distribution law of
nonextensive statistics and this result is independent of the initial
configurations considered.Comment: 3 page, 1 figure, proceedings of the X Marcel Grossmann Meeting 22-26
July, 2003, Rio de Janeir
Einstein equations in the null quasi-spherical gauge
The structure of the full Einstein equations in a coordinate gauge based on
expanding null hypersurfaces foliated by metric 2-spheres is explored. The
simple form of the resulting equations has many applications -- in the present
paper we describe the structure of timelike boundary conditions; the matching
problem across null hypersurfaces; and the propagation of gravitational shocks.Comment: 12 pages, LaTeX (revtex, amssymb), revision 18 pages, contains
expanded discussion and explanations, updated references, to appear in CQ
(2,2)-Formalism of General Relativity: An Exact Solution
I discuss the (2,2)-formalism of general relativity based on the
(2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian
signature. In this formalism general relativity is describable as a Yang-Mills
gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge
symmetry is the group of the diffeomorphisms of the 2-dimensional fibre
manifold. After presenting the Einstein's field equations in this formalism, I
solve them for spherically symmetric case to obtain the Schwarzschild solution.
Then I discuss possible applications of this formalism.Comment: 2 figures included, IOP style file neede
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