41 research outputs found
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
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
Gluing Initial Data Sets for General Relativity
We establish an optimal gluing construction for general relativistic initial
data sets. The construction is optimal in two distinct ways. First, it applies
to generic initial data sets and the required (generically satisfied)
hypotheses are geometrically and physically natural. Secondly, the construction
is completely local in the sense that the initial data is left unaltered on the
complement of arbitrarily small neighborhoods of the points about which the
gluing takes place. Using this construction we establish the existence of
cosmological, maximal globally hyperbolic, vacuum space-times with no constant
mean curvature spacelike Cauchy surfaces.Comment: Final published version - PRL, 4 page
A Remark on Boundary Effects in Static Vacuum Initial Data sets
Let (M, g) be an asymptotically flat static vacuum initial data set with
non-empty compact boundary. We prove that (M, g) is isometric to a spacelike
slice of a Schwarzschild spacetime under the mere assumption that the boundary
of (M, g) has zero mean curvature, hence generalizing a classic result of
Bunting and Masood-ul-Alam. In the case that the boundary has constant positive
mean curvature and satisfies a stability condition, we derive an upper bound of
the ADM mass of (M, g) in terms of the area and mean curvature of the boundary.
Our discussion is motivated by Bartnik's quasi-local mass definition.Comment: 10 pages, to be published in Classical and Quantum Gravit
Solutions of special asymptotics to the Einstein constraint equations
We construct solutions with prescribed asymptotics to the Einstein constraint
equations using a cut-off technique. Moreover, we give various examples of
vacuum asymptotically flat manifolds whose center of mass and angular momentum
are ill-defined.Comment: 13 pages; the error in Lemma 3.5 fixed and typos corrected; to appear
in Class. Quantum Gra
On the Nature of Singularities in Plane Symmetric Scalar Field Cosmologies
The nature of the initial singularity in spatially compact plane symmetric
scalar field cosmologies is investigated. It is shown that this singularity is
crushing and velocity dominated and that the Kretschmann scalar diverges
uniformly as it is approached. The last fact means in particular that a maximal
globally hyperbolic spacetime in this class cannot be extended towards the past
through a Cauchy horizon. A subclass of these spacetimes is identified for
which the singularity is isotropic.Comment: 7 pages, MPA-AR-94-
Rotating solitons and non-rotating, non-static black holes
It is shown that the non-Abelian black hole solutions have stationary
generalizations which are parameterized by their angular momentum and electric
Yang-Mills charge. In particular, there exists a non-static class of stationary
black holes with vanishing angular momentum. It is also argued that the
particle-like Bartnik-McKinnon solutions admit slowly rotating, globally
regular excitations. In agreement with the non-Abelian version of the staticity
theorem, these non-static soliton excitations carry electric charge, although
their non-rotating limit is neutral.Comment: 5 pages, REVTe
Slowly Rotating Non-Abelian Black Holes
It is shown that the well-known non-Abelian static SU(2) black hole solutions
have rotating generalizations, provided that the hypothesis of linearization
stability is accepted. Surprisingly, this rotating branch has an asymptotically
Abelian gauge field with an electric charge that cannot vanish, although the
non-rotating limit is uncharged. We argue that this may be related to our
second finding, namely that there are no globally regular slowly rotating
excitations of the particle-like Bartnik-McKinnon solutions.Comment: 8 pages, LaTe
Dain's invariant on non-time symmetric initial data sets
We extend Dain's construction of a geometric invariant characterising static
initial data sets for the vacuum Einstein field equations to situations with a
non-vanishing extrinsic curvature. This invariant gives a measure of how much
the initial data sets deviates from stationarity. In particular, it vanishes if
and only if the initial data set is stationary. Thus, the invariant provides a
quantification of the amount of gravitational radiation contained in the
initial data set
Deformations of the hemisphere that increase scalar curvature
Consider a compact Riemannian manifold M of dimension n whose boundary
\partial M is totally geodesic and is isometric to the standard sphere S^{n-1}.
A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at
least n(n-1), then M is isometric to the hemisphere S_+^n equipped with its
standard metric. This conjecture is inspired by the positive mass theorem in
general relativity, and has been verified in many special cases. In this paper,
we construct counterexamples to Min-Oo's conjecture in dimension n \geq 3.Comment: Revised version, to appear in Invent. Mat