716 research outputs found
Local and Global Analytic Solutions for a Class of Characteristic Problems of the Einstein Vacuum Equations in the "Double Null Foliation Gauge"
The main goal of this work consists in showing that the analytic solutions
for a class of characteristic problems for the Einstein vacuum equations have
an existence region larger than the one provided by the Cauchy-Kowalevski
theorem due to the intrinsic hyperbolicity of the Einstein equations. To prove
this result we first describe a geometric way of writing the vacuum Einstein
equations for the characteristic problems we are considering, in a gauge
characterized by the introduction of a double null cone foliation of the
spacetime. Then we prove that the existence region for the analytic solutions
can be extended to a larger region which depends only on the validity of the
apriori estimates for the Weyl equations, associated to the "Bel-Robinson
norms". In particular if the initial data are sufficiently small we show that
the analytic solution is global. Before showing how to extend the existence
region we describe the same result in the case of the Burger equation, which,
even if much simpler, nevertheless requires analogous logical steps required
for the general proof. Due to length of this work, in this paper we mainly
concentrate on the definition of the gauge we use and on writing in a
"geometric" way the Einstein equations, then we show how the Cauchy-Kowalevski
theorem is adapted to the characteristic problem for the Einstein equations and
we describe how the existence region can be extended in the case of the Burger
equation. Finally we describe the structure of the extension proof in the case
of the Einstein equations. The technical parts of this last result is the
content of a second paper.Comment: 68 page
Quantization of Gauge Field Theories on the Front-Form without Gauge Constraints I : The Abelian Case
Recently, we have proposed a new front-form quantization which treated both
the and the coordinates as front-form 'times.' This
quantization was found to preserve parity explicitly. In this paper we extend
this construction to local Abelian gauge fields . We quantize this theory using
a method proposed originally by Faddeev and Jackiw . We emphasize here the
feature that quantizing along both and , gauge theories does not
require extra constraints (also known as 'gauge conditions') to determine the
solution uniquely.Comment: 18 pages, phyzz
On the existence of Killing vector fields
In covariant metric theories of coupled gravity-matter systems the necessary
and sufficient conditions ensuring the existence of a Killing vector field are
investigated. It is shown that the symmetries of initial data sets are
preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra
Ghost points in inverse scattering constructions of stationary Einstein metrics
We prove a removable singularities theorem for stationary Einstein equations,
with useful implications for constructions of stationary solutions using
soliton methods
Rolling friction of a viscous sphere on a hard plane
A first-principle continuum-mechanics expression for the rolling friction
coefficient is obtained for the rolling motion of a viscoelastic sphere on a
hard plane. It relates the friction coefficient to the viscous and elastic
constants of the sphere material. The relation obtained refers to the case when
the deformation of the sphere is small, the velocity of the sphere is
much less than the speed of sound in the material and when the characteristic
time is much larger than the dissipative relaxation times of the
viscoelastic material. To our knowledge this is the first ``first-principle''
expression of the rolling friction coefficient which does not contain empirical
parameters.Comment: 6 pages, 2 figure
Uniqueness properties of the Kerr metric
We obtain a geometrical condition on vacuum, stationary, asymptotically flat
spacetimes which is necessary and sufficient for the spacetime to be locally
isometric to Kerr. Namely, we prove a theorem stating that an asymptotically
flat, stationary, vacuum spacetime such that the so-called Killing form is an
eigenvector of the self-dual Weyl tensor must be locally isometric to Kerr.
Asymptotic flatness is a fundamental hypothesis of the theorem, as we
demonstrate by writing down the family of metrics obtained when this
requirement is dropped. This result indicates why the Kerr metric plays such an
important role in general relativity. It may also be of interest in order to
extend the uniqueness theorems of black holes to the non-connected and to the
non-analytic case.Comment: 30 pages, LaTeX, submitted to Classical and Quantum Gravit
Uniqueness Theorem of Static Degenerate and Non-degenerate Charged Black Holes in Higher Dimensions
We prove the uniqueness theorem for static higher dimensional charged black
holes spacetime containing an asymptotically flat spacelike hypersurface with
compact interior and with both degenerate and non-degenerate components of the
event horizon.Comment: 9 pages, RevTex, to be published in Phys.Rev.D1
Uniqueness Theorem for Static Black Hole Solutions of sigma-models in Higher Dimensions
We prove the uniqueness theorem for self-gravitating non-linear sigma-models
in higher dimensional spacetime. Applying the positive mass theorem we show
that Schwarzschild-Tagherlini spacetime is the only maximally extended, static
asymptotically flat solution with non-rotating regular event horizon with a
constant mapping.Comment: 5 peges, Revtex, to be published in Class.Quantum Gra
Extrema of Mass, First Law of Black Hole Mechanics and Staticity Theorem in Einstein-Maxwell-axion-dilaton Gravity
Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we
derived the formulas for the variation of mass and other asymptotic conserved
quantities in the theory under consideration. Generalizing this kind of
reasoning to the initial dota for the manifold with an interior boundary we got
the generalized first law of black hole mechanics. We consider an
asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity
describing a black hole with a Killing vector field timelike at infinity, the
horizon of which comprises a bifurcate Killing horizon with a bifurcate
surface. Supposing that the Killing vector field is asymptotically orthogonal
to the static hypersurface with boundary S and compact interior, we find that
the solution is static in the exterior world, when the timelike vector field is
normal to the horizon and has vanishing electric and axion- electric fields on
static slices.Comment: 17 pages, Revtex, a few comments (introduction) and references adde
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