264 research outputs found
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
Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times
We prove upper bounds on angular momentum and centre of mass in terms of the
Hamiltonian mass and cosmological constant for non-singular asymptotically
anti-de Sitter initial data sets satisfying the dominant energy condition. We
work in all space-dimensions larger than or equal to three, and allow a large
class of asymptotic backgrounds, with spherical and non-spherical conformal
infinities; in the latter case, a spin-structure compatibility condition is
imposed. We give a large class of non-trivial examples saturating the
inequality. We analyse exhaustively the borderline case in space-time dimension
four: for spherical cross-sections of Scri, equality together with completeness
occurs only in anti-de Sitter space-time. On the other hand, in the toroidal
case, regular non-trivial initial data sets saturating the bound exist.Comment: improvements in the presentation; some statements correcte
On non-existence of static vacuum black holes with degenerate components of the event horizon
We present a simple proof of the non-existence of degenerate components of
the event horizon in static, vacuum, regular, four-dimensional black hole
spacetimes. We discuss the generalisation to higher dimensions and the
inclusion of a cosmological constant.Comment: latex2e, 9 pages in A
Conditions for nonexistence of static or stationary, Einstein-Maxwell, non-inheriting black-holes
We consider asymptotically-flat, static and stationary solutions of the
Einstein equations representing Einstein-Maxwell space-times in which the
Maxwell field is not constant along the Killing vector defining stationarity,
so that the symmetry of the space-time is not inherited by the electromagnetic
field. We find that static degenerate black hole solutions are not possible
and, subject to stronger assumptions, nor are static, non-degenerate or
stationary black holes. We describe the possibilities if the stronger
assumptions are relaxed.Comment: 19 pages, to appear in GER
Topological censorship for Kaluza-Klein space-times
The standard topological censorship theorems require asymptotic hypotheses
which are too restrictive for several situations of interest. In this paper we
prove a version of topological censorship under significantly weaker
conditions, compatible e.g. with solutions with Kaluza-Klein asymptotic
behavior. In particular we prove simple connectedness of the quotient of the
domain of outer communications by the group of symmetries for models which are
asymptotically flat, or asymptotically anti-de Sitter, in a Kaluza-Klein sense.
This allows one, e.g., to define the twist potentials needed for the reduction
of the field equations in uniqueness theorems. Finally, the methods used to
prove the above are used to show that weakly trapped compact surfaces cannot be
seen from Scri.Comment: minor correction
On smoothness-asymmetric null infinities
We discuss the existence of asymptotically Euclidean initial data sets to the
vacuum Einstein field equations which would give rise (modulo an existence
result for the evolution equations near spatial infinity) to developments with
a past and a future null infinity of different smoothness. For simplicity, the
analysis is restricted to the class of conformally flat, axially symmetric
initial data sets. It is shown how the free parameters in the second
fundamental form of the data can be used to satisfy certain obstructions to the
smoothness of null infinity. The resulting initial data sets could be
interpreted as those of some sort of (non-linearly) distorted Schwarzschild
black hole. Its developments would be so that they admit a peeling future null
infinity, but at the same time have a polyhomogeneous (non-peeling) past null
infinity.Comment: 13 pages, 1 figur
Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem
We study Killing vector fields in asymptotically flat space-times. We prove
the following result, implicitly assumed in the uniqueness theory of stationary
black holes. If the conditions of the rigidity part of the positive energy
theorem are met, then in such space-times there are no asymptotically null
Killing vector fields except if the initial data set can be embedded in
Minkowski space-time. We also give a proof of the non-existence of non-singular
(in an appropriate sense) asymptotically flat space-times which satisfy an
energy condition and which have a null ADM four-momentum, under conditions
weaker than previously considered.Comment: 30 page
Uniqueness of the mass in the radiating regime
The usual approaches to the definition of energy give an ambiguous result for
the energy of fields in the radiating regime. We show that for a massless
scalar field in Minkowski space-time the definition may be rendered unambiguous
by adding the requirement that the energy cannot increase in retarded time. We
present a similar theorem for the gravitational field, proved elsewhere, which
establishes that the Trautman-Bondi energy is the unique (up to a
multiplicative factor) functional, within a natural class, which is monotonic
in time for all solutions of the vacuum Einstein equations admitting a smooth
``piece'' of conformal null infinity Scri.Comment: 8 pages, revte
Towards the classification of static vacuum spacetimes with negative cosmological constant
We present a systematic study of static solutions of the vacuum Einstein
equations with negative cosmological constant which asymptotically approach the
generalized Kottler (``Schwarzschild--anti-de Sitter'') solution, within
(mainly) a conformal framework. We show connectedness of conformal infinity for
appropriately regular such space-times. We give an explicit expression for the
Hamiltonian mass of the (not necessarily static) metrics within the class
considered; in the static case we show that they have a finite and well defined
Hawking mass. We prove inequalities relating the mass and the horizon area of
the (static) metrics considered to those of appropriate reference generalized
Kottler metrics. Those inequalities yield an inequality which is opposite to
the conjectured generalized Penrose inequality. They can thus be used to prove
a uniqueness theorem for the generalized Kottler black holes if the generalized
Penrose inequality can be established.Comment: the discussion of our results includes now some solutions of Horowitz
and Myers; typos corrected here and there; a shortened version of this
version will appear in Journal of Mathematical Physic
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