1,613 research outputs found
Particle-Like Solutions of the Einstein-Dirac Equations
The coupled Einstein-Dirac equations for a static, spherically symmetric
system of two fermions in a singlet spinor state are derived. Using numerical
methods, we construct an infinite number of soliton-like solutions of these
equations. The stability of the solutions is analyzed. For weak coupling (i.e.,
small rest mass of the fermions), all the solutions are linearly stable (with
respect to spherically symmetric perturbations), whereas for stronger coupling,
both stable and unstable solutions exist. For the physical interpretation, we
discuss how the energy of the fermions and the (ADM) mass behave as functions
of the rest mass of the fermions. Although gravitation is not renormalizable,
our solutions of the Einstein-Dirac equations are regular and well-behaved even
for strong coupling.Comment: 31 pages, LaTeX, 21 PostScript figures, some references adde
An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry
We consider the scalar wave equation in the Kerr geometry for Cauchy data
which is smooth and compactly supported outside the event horizon. We derive an
integral representation which expresses the solution as a superposition of
solutions of the radial and angular ODEs which arise in the separation of
variables. In particular, we prove completeness of the solutions of the
separated ODEs.
This integral representation is a suitable starting point for a detailed
analysis of the long-time dynamics of scalar waves in the Kerr geometry.Comment: 41 pages, 4 figures, minor correction
Global behavior of solutions to the static spherically symmetric EYM equations
The set of all possible spherically symmetric magnetic static
Einstein-Yang-Mills field equations for an arbitrary compact semi-simple gauge
group was classified in two previous papers. Local analytic solutions near
the center and a black hole horizon as well as those that are analytic and
bounded near infinity were shown to exist. Some globally bounded solutions are
also known to exist because they can be obtained by embedding solutions for the
case which is well understood. Here we derive some asymptotic
properties of an arbitrary global solution, namely one that exists locally near
a radial value , has positive mass at and develops no
horizon for all . The set of asymptotic values of the Yang-Mills
potential (in a suitable well defined gauge) is shown to be finite in the
so-called regular case, but may form a more complicated real variety for models
obtained from irregular rotation group actions.Comment: 43 page
Cosmological Analogues of the Bartnik--McKinnon Solutions
We present a numerical classification of the spherically symmetric, static
solutions to the Einstein--Yang--Mills equations with cosmological constant
. We find three qualitatively different classes of configurations,
where the solutions in each class are characterized by the value of
and the number of nodes, , of the Yang--Mills amplitude. For sufficiently
small, positive values of the cosmological constant, \Lambda < \Llow(n), the
solutions generalize the Bartnik--McKinnon solitons, which are now surrounded
by a cosmological horizon and approach the deSitter geometry in the asymptotic
region. For a discrete set of values , the solutions are topologically --spheres, the ground state
being the Einstein Universe. In the intermediate region, that is for
\Llow(n) < \Lambda < \Lhig(n), there exists a discrete family of global
solutions with horizon and ``finite size''.Comment: 16 pages, LaTeX, 9 Postscript figures, uses epsf.st
Local existence of dynamical and trapping horizons
Given a spacelike foliation of a spacetime and a marginally outer trapped
surface S on some initial leaf, we prove that under a suitable stability
condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by
marginally outer trapped slices which lie in the leaves of the given foliation.
We also show that under rather weak energy conditions this horizon must be
either achronal or spacelike everywhere. Furthermore, we discuss the relation
between ``bounding'' and ``stability'' properties of marginally outer trapped
surfaces.Comment: 4 pages, 1 figure, minor change
Hairy Black Holes, Horizon Mass and Solitons
Properties of the horizon mass of hairy black holes are discussed with
emphasis on certain subtle and initially unexpected features. A key property
suggests that hairy black holes may be regarded as `bound states' of ordinary
black holes without hair and colored solitons. This model is then used to
predict the qualitative behavior of the horizon properties of hairy black
holes, to provide a physical `explanation' of their instability and to put
qualitative constraints on the end point configurations that result from this
instability. The available numerical calculations support these predictions.
Furthermore, the physical arguments are robust and should be applicable also in
more complicated situations where detailed numerical work is yet to be carried
out.Comment: 25 pages, 5 (new) figures. Revtex file. Final version to appear in
CQ
Symmetry-breaking under small perturbations
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46160/1/205_2005_Article_BF01055753.pd
Psychiatric genetics and the structure of psychopathology
For over a century, psychiatric disorders have been defined by expert opinion and clinical observation. The modern DSM has relied on a consensus of experts to define categorical syndromes based on clusters of symptoms and signs, and, to some extent, external validators, such as longitudinal course and response to treatment. In the absence of an established etiology, psychiatry has struggled to validate these descriptive syndromes, and to define the boundaries between disorders and between normal and pathologic variation. Recent advances in genomic research, coupled with large-scale collaborative efforts like the Psychiatric Genomics Consortium, have identified hundreds of common and rare genetic variations that contribute to a range of neuropsychiatric disorders. At the same time, they have begun to address deeper questions about the structure and classification of mental disorders: To what extent do genetic findings support or challenge our clinical nosology? Are there genetic boundaries between psychiatric and neurologic illness? Do the data support a boundary between disorder and normal variation? Is it possible to envision a nosology based on genetically informed disease mechanisms? This review provides an overview of conceptual issues and genetic findings that bear on the relationships among and boundaries between psychiatric disorders and other conditions. We highlight implications for the evolving classification of psychopathology and the challenges for clinical translation
Absence of Stationary, Spherically Symmetric Black Hole Solutions for Einstein-Dirac-Yang/Mills Equations with Angular Momentum
We study a stationary, spherically symmetric system of (2j+1) massive Dirac particles, each having angular momentum j, j=1,2,..., in a classical gravitational and SU(2) Yang-Mills field. We show that for any black hole solution of the associated Einstein-Dirac-Yang/Mills equations, the spinors must vanish identically outside of the event horizon
On all possible static spherically symmetric EYM solitons and black holes
We prove local existence and uniqueness of static spherically symmetric
solutions of the Einstein-Yang-Mills equations for any action of the rotation
group (or SU(2)) by automorphisms of a principal bundle over space-time whose
structure group is a compact semisimple Lie group G. These actions are
characterized by a vector in the Cartan subalgebra of g and are called regular
if the vector lies in the interior of a Weyl chamber. In the irregular cases
(the majority for larger gauge groups) the boundary value problem that results
for possible asymptotically flat soliton or black hole solutions is more
complicated than in the previously discussed regular cases. In particular,
there is no longer a gauge choice possible in general so that the Yang-Mills
potential can be given by just real-valued functions. We prove the local
existence of regular solutions near the singularities of the system at the
center, the black hole horizon, and at infinity, establish the parameters that
characterize these local solutions, and discuss the set of possible actions and
the numerical methods necessary to search for global solutions. That some
special global solutions exist is easily derived from the fact that su(2) is a
subalgebra of any compact semisimple Lie algebra. But the set of less trivial
global solutions remains to be explored.Comment: 26 pages, 2 figures, LaTeX, misprints corrected, 1 reference adde
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