728 research outputs found
Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass
We extend the validity of Brill's axisymmetric positive energy theorem to all
asymptotically flat initial data sets with positive scalar curvature on simply
connected manifolds.Comment: 33 pages in A
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
On periodic solutions of nonlinear wave equations, including Einstein equations with a negative cosmological constant
We construct periodic solutions of nonlinear wave equations using analytic
continuation. The construction applies in particular to Einstein equations,
leading to infinite-dimensional families of time-periodic solutions of the
vacuum, or of the Einstein-Maxwell-dilaton-scalar
fields-Yang-Mills-Higgs-Chern-Simons- equations, with a negative
cosmological constant.Comment: 15 pages, 1 figur
On higher dimensional black holes with abelian isometry group
We consider (n+1)--dimensional, stationary, asymptotically flat, or
Kaluza-Klein asymptotically flat black holes, with an abelian --dimensional
subgroup of the isometry group satisfying an orthogonal integrability
condition. Under suitable regularity conditions we prove that the area of the
group orbits is positive on the domain of outer communications, vanishing only
on its boundary and on the "symmetry axis". We further show that the orbits of
the connected component of the isometry group are timelike throughout the
domain of outer communications. Those results provide a starting point for the
classification of such black holes. Finally, we show non-existence of zeros of
static Killing vectors on degenerate Killing horizons, as needed for the
generalisation of the static no-hair theorem to higher dimensions
Convexity of reduced energy and mass angular momentum inequalities
In this paper, we extend the work in
\cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic
conditions on the second fundamental form, and we also give an norm
bound for the difference between general data and Extreme Kerr data or Extreme
Kerr-Newman data by proving convexity of the renormalized Dirichlet energy when
the target has non-positive curvature. In particular, we give the first proof
of the strict mass/angular momentum/charge inequality for axisymmetric
Einstein/Maxwell data which is not identical with the extreme Kerr-Newman
solution.Comment: 27 page
Geometric invariance of mass-like asymptotic invariants
We study coordinate-invariance of some asymptotic invariants such as the ADM
mass or the Chru\'sciel-Herzlich momentum, given by an integral over a
"boundary at infinity". When changing the coordinates at infinity, some terms
in the change of integrand do not decay fast enough to have a vanishing
integral at infinity; but they may be gathered in a divergence, thus having
vanishing integral over any closed hypersurface. This fact could only be
checked after direct calculation (and was called a "curious cancellation"). We
give a conceptual explanation thereof.Comment: 13 page
On Israel-Wilson-Perjes black holes
We show, under certain conditions, that regular Israel-Wilson-Perj\'es black
holes necessarily belong to the Majumdar-Papapetrou family
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