13 research outputs found
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
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 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-
Total angular momentum from Dirac eigenspinors
The eigenvalue problem for Dirac operators, constructed from two connections
on the spinor bundle over closed spacelike 2-surfaces, is investigated. A class
of divergence free vector fields, built from the eigenspinors, are found,
which, for the lowest eigenvalue, reproduce the rotation Killing vectors of
metric spheres, and provide rotation BMS vector fields at future null infinity.
This makes it possible to introduce a well defined, gauge invariant spatial
angular momentum at null infinity, which reduces to the standard expression in
stationary spacetimes. The general formula for the angular momentum flux
carried away be the gravitational radiation is also derived.Comment: 34 pages, typos corrected, four references added, appearing in Class.
Quantum Gra
Stringy Robinson-Trautman Solutions
A class of solutions of the low energy string theory in four dimensions is
studied. This class admits a geodesic, shear-free null congruence which is
non-twisting but in general diverging and the corresponding solutions in
Einstein's theory form the Robinson-Trautman family together with a subset of
the Kundt's class. The Robinson-Trautman conditions are found to be frame
invariant in string theory. The Lorentz Chern-Simons three form of the stringy
Robinson-Trautman solutions is shown to be always closed. The stringy
generalizations of the vacuum Robinson-Trautman equation are obtained and three
subclasses of solutions are identified. One of these subclasses exists, among
all the dilatonic theories, only in Einstein's theory and in string theory.
Several known solutions including the dilatonic black holes, the pp- waves, the
stringy C-metric and certain solutions which correspond to exact conformal
field theories are shown to be particular members of the stringy
Robinson-Trautman family. Some new solutions which are static or asymptotically
flat and radiating are also presented. The radiating solutions have a positive
Bondi mass. One of these radiating solutions has the property that it settles
down smoothly to a black hole state at late retarded times.Comment: Latex, 30 Pages, 1 Figure; to appear in Phys. Rev.
Numerical Approaches to Spacetime Singularities
This Living Review updates a previous version which its itself an update of a
review article. Numerical exploration of the properties of singularities could,
in principle, yield detailed understanding of their nature in physically
realistic cases. Examples of numerical investigations into the formation of
naked singularities, critical behavior in collapse, passage through the Cauchy
horizon, chaos of the Mixmaster singularity, and singularities in spatially
inhomogeneous cosmologies are discussed.Comment: 51 pages, 6 figures may be found in online version: Living Rev.
Relativity 2002-1 at www.livingreviews.or
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local-in-time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity that offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure or late-time asymptotics are given. A
conjectural picture of the asymptotic behaviour of general cosmological
solutions of the Einstein equations is built up. Some miscellaneous topics
connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living
Rev. Rel. 5 (2002)
Black Holes in Higher Dimensions
We review black hole solutions of higher-dimensional vacuum gravity, and of
higher-dimensional supergravity theories. The discussion of vacuum gravity is
pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and
solution-generating techniques. We discuss black hole solutions of maximal
supergravity theories, including black holes in anti-de Sitter space. General
results and open problems are discussed throughout.Comment: 76 pages, 14 figures; review article for Living Reviews in
Relativity. v2: some improvements and refs adde