26 research outputs found
A poor man's positive energy theorem: II. Null geodesics
We show that positivity of energy for stationary, or strongly uniformly
Schwarzschildian, asymptotically flat, non-singular domains of outer
communications can be proved using Galloway's null rigidity theorem.Comment: Latex2e, 24 A4 pages, minor change
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
On "many black hole" space-times
We analyze the horizon structure of families of space times obtained by
evolving initial data sets containing apparent horizons with several connected
components. We show that under certain smallness conditions the outermost
apparent horizons will also have several connected components. We further show
that, again under a smallness condition, the maximal globally hyperbolic
development of the many black hole initial data constructed by Chrusciel and
Delay, or of hyperboloidal data of Isenberg, Mazzeo and Pollack, will have an
event horizon, the intersection of which with the initial data hypersurface is
not connected. This justifies the "many black hole" character of those
space-times.Comment: several graphic file
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
On the area of the symmetry orbits in symmetric spacetimes with Vlasov matter
This paper treats the global existence question for a collection of general
relativistic collisionless particles, all having the same mass. The spacetimes
considered are globally hyperbolic, with Cauchy surface a 3-torus. Furthermore,
the spacetimes considered are isometrically invariant under a two-dimensional
group action, the orbits of which are spacelike 2-tori. It is known from
previous work that the area of the group orbits serves as a global time
coordinate. In the present work it is shown that the area takes on all positive
values in the maximal Cauchy development.Comment: 27 pages, version 2 minor changes and correction
Lagrangian and Hamiltonian for the Bondi-Sachs metrics
We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the
Einstein vacuum equations in a closed form. Following the Dirac approach to
constrained systems we investigate the related Hamiltonian formulation.Comment: 8 page
Global existence problem in -Gowdy symmetric IIB superstring cosmology
We show global existence theorems for Gowdy symmetric spacetimes with type
IIB stringy matter. The areal and constant mean curvature time coordinates are
used. Before coming to that, it is shown that a wave map describes the
evolution of this system
CYK Tensors, Maxwell Field and Conserved Quantities for Spin-2 Field
Starting from an important application of Conformal Yano--Killing tensors for
the existence of global charges in gravity, some new observations at \scri^+
are given. They allow to define asymptotic charges (at future null infinity) in
terms of the Weyl tensor together with their fluxes through \scri^+. It
occurs that some of them play a role of obstructions for the existence of
angular momentum.
Moreover, new relations between solutions of the Maxwell equations and the
spin-2 field are given. They are used in the construction of new conserved
quantities which are quadratic in terms of the Weyl tensor. The obtained
formulae are similar to the functionals obtained from the
Bel--Robinson tensor.Comment: 20 pages, LaTe
On the area of the symmetry orbits in symmetric spacetimes
We obtain a global existence result for the Einstein equations. We show that
in the maximal Cauchy development of vacuum symmetric initial data with
nonvanishing twist constant, except for the special case of flat Kasner initial
data, the area of the group orbits takes on all positive values. This
result shows that the areal time coordinate which covers these spacetimes
runs from zero to infinity, with the singularity occurring at R=0.Comment: The appendix which appears in version 1 has a technical problem (the
inequality appearing as the first stage of (52) is not necessarily true), and
since the appendix is unnecessary for the proof of our results, we leave it
out. version 2 -- clarifications added, version 3 -- reference correcte
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