458 research outputs found
Global Foliations of Vacuum Spacetimes with Isometry
We prove a global existence theorem (with respect to a geometrically- defined
time) for globally hyperbolic solutions of the vacuum Einstein equations which
admit a isometry group with two-dimensional spacelike orbits, acting on
spacelike surfaces.Comment: 38 pages, 0 figures, LaTe
Global constants in (2+1)--dimensional gravity
The extended conformal algebra (so)(2,3) of global, quantum, constants of
motion in 2+1 dimensional gravity with topology R x T^2 and negative
cosmological constant is reviewed. It is shown that the 10 global constants
form a complete set by expressing them in terms of two commuting spinors and
the Dirac gamma matrices. The spinor components are the globally constant
holonomy parameters, and their respective spinor norms are their quantum
commutators.Comment: 14 pages, to appear in Classical and Quantum Gravity, Spacetime
Safari: Essays in Honor of Vincent Moncrief on the Classical Physics of
Strong Gravitational Field
Cauchy horizons in Gowdy space times
We analyse exhaustively the structure of \emph{non-degenerate} Cauchy
horizons in Gowdy space-times, and we establish existence of a large class of
non-polarized Gowdy space-times with such horizons.
Added in proof: Our results here, together with deep new results of H.
Ringstr\"om (talk at the Miami Waves conference, January 2004), establish
strong cosmic censorship in (toroidal) Gowdy space-times.Comment: 25 pages Latex. Further information at http://grtensor.org/gowdy
Perturbations of Spatially Closed Bianchi III Spacetimes
Motivated by the recent interest in dynamical properties of topologically
nontrivial spacetimes, we study linear perturbations of spatially closed
Bianchi III vacuum spacetimes, whose spatial topology is the direct product of
a higher genus surface and the circle. We first develop necessary mode
functions, vectors, and tensors, and then perform separations of (perturbation)
variables. The perturbation equations decouple in a way that is similar to but
a generalization of those of the Regge--Wheeler spherically symmetric case. We
further achieve a decoupling of each set of perturbation equations into
gauge-dependent and independent parts, by which we obtain wave equations for
the gauge-invariant variables. We then discuss choices of gauge and stability
properties. Details of the compactification of Bianchi III manifolds and
spacetimes are presented in an appendix. In the other appendices we study
scalar field and electromagnetic equations on the same background to compare
asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear
in Class. Quant. Gravi
Gravitational waves in general relativity: XIV. Bondi expansions and the ``polyhomogeneity'' of \Scri
The structure of polyhomogeneous space-times (i.e., space-times with metrics
which admit an expansion in terms of ) constructed by a
Bondi--Sachs type method is analysed. The occurrence of some log terms in an
asymptotic expansion of the metric is related to the non--vanishing of the Weyl
tensor at Scri. Various quantities of interest, including the Bondi mass loss
formula, the peeling--off of the Riemann tensor and the Newman--Penrose
constants of motion are re-examined in this context.Comment: LaTeX, 28pp, CMA-MR14-9
The generalization of the Regge-Wheeler equation for self-gravitating matter fields
It is shown that the dynamical evolution of perturbations on a static
spacetime is governed by a standard pulsation equation for the extrinsic
curvature tensor. The centerpiece of the pulsation equation is a wave operator
whose spatial part is manifestly self-adjoint. In contrast to metric
formulations, the curvature-based approach to gravitational perturbation theory
generalizes in a natural way to self-gravitating matter fields. For a certain
relevant subspace of perturbations the pulsation operator is symmetric with
respect to a positive inner product and therefore allows spectral theory to be
applied. In particular, this is the case for odd-parity perturbations of
spherically symmetric background configurations. As an example, the pulsation
equations for self-gravitating, non-Abelian gauge fields are explicitly shown
to be symmetric in the gravitational, the Yang Mills, and the off-diagonal
sector.Comment: 4 pages, revtex, no figure
Ashtekar Variables in Classical General Realtivity
This paper contains an introduction into Ashtekar's reformulation of General
Relativity in terms of connection variables. To appear in "Canonical Gravity -
From Classical to Quantum", ed. by J. Ehlers and H. Friedrich, Springer Verlag
(1994).Comment: 31 Pages, Plain-Tex; Further comments were added, minor grammatical
changes made and typos correcte
Entropic-acoustic instability of shocked Bondi accretion I. What does perturbed Bondi accretion sound like ?
In the radial flow of gas into a black hole (i.e. Bondi accretion), the
infall of any entropy or vorticity perturbation produces acoustic waves
propagating outward. The dependence of this acoustic flux on the shape of the
perturbation is investigated in detail. This is the key process in the
mechanism of the entropic-acoustic instability proposed by Foglizzo & Tagger
(2000) to explain the instability of Bondi-Hoyle-Lyttleton accretion. These
acoustic waves create new entropy and vorticity perturbations when they reach
the shock, thus closing the entropic-acoustic cycle. With an adiabatic index
1<gamma<=5/3, the linearized equations describing the perturbations of the
Bondi flow are studied analytically and solved numerically. The fundamental
frequency of this problem is the cut-off frequency of acoustic refraction,
below which ingoing acoustic waves are refracted out. This cut-off is
significantly smaller than the Keplerian frequency at the sonic radius and
depends on the latitudinal number l of the perturbations. When advected
adiabatically inward, entropy and vorticity perturbations trigger acoustic
waves propagating outward, with an efficiency which is highest for non radial
perturbations l=1. The outgoing acoustic flux produced by the advection of
vorticity perturbations is always moderate and peaks at rather low frequency.
By contrast, the acoustic flux produced by an entropy wave is highest close to
the refraction cut-off. It can be very large if gamma is close to 5/3. These
results suggest that the shocked Bondi flow with gamma=5/3 is strongly unstable
with respect to the entropic-acoustic mechanism.Comment: 14 pages, 11 figures, accepted for publication in A&
On Further Generalization of the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
A rigidity theorem that applies to smooth electrovac spacetimes which
represent either (A) an asymptotically flat stationary black hole or (B) a
cosmological spacetime with a compact Cauchy horizon ruled by closed null
geodesics was given in a recent work \cite{frw}. Here we enlarge the framework
of the corresponding investigations by allowing the presence of other type of
matter fields. In the first part the matter fields are involved merely
implicitly via the assumption that the dominant energy condition is satisfied.
In the second part Einstein-Klein-Gordon (EKG), Einstein-[non-Abelian] Higgs
(E[nA]H), Einstein-[Maxwell]-Yang-Mills-dilaton (E[M]YMd) and
Einstein-Yang-Mills-Higgs (EYMH) systems are studied. The black hole event
horizon or, respectively, the compact Cauchy horizon of the considered
spacetimes is assumed to be a smooth non-degenerate null hypersurface. It is
proven that there exists a Killing vector field in a one-sided neighborhood of
the horizon in EKG, E[nA]H, E[M]YMd and EYMH spacetimes. This Killing vector
field is normal to the horizon, moreover, the associated matter fields are also
shown to be invariant with respect to it. The presented results provide
generalizations of the rigidity theorems of Hawking (for case A) and of
Moncrief and Isenberg (for case B) and, in turn, they strengthen the validity
of both the black hole rigidity scenario and the strong cosmic censor
conjecture of classical general relativity.Comment: 25 pages, LaTex, a shortened version, including a new proof for lemma
5.1, the additional case of Einstein-Yang-Mills-Higgs systems is also
covered, to appear in Class. Quant. Gra
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