168 research outputs found
Analytic Continuation for Asymptotically AdS 3D Gravity
We have previously proposed that asymptotically AdS 3D wormholes and black
holes can be analytically continued to the Euclidean signature. The analytic
continuation procedure was described for non-rotating spacetimes, for which a
plane t=0 of time symmetry exists. The resulting Euclidean manifolds turned out
to be handlebodies whose boundary is the Schottky double of the geometry of the
t=0 plane. In the present paper we generalize this analytic continuation map to
the case of rotating wormholes. The Euclidean manifolds we obtain are quotients
of the hyperbolic space by a certain quasi-Fuchsian group. The group is the
Fenchel-Nielsen deformation of the group of the non-rotating spacetime. The
angular velocity of an asymptotic region is shown to be related to the
Fenchel-Nielsen twist. This solves the problem of classification of rotating
black holes and wormholes in 2+1 dimensions: the spacetimes are parametrized by
the moduli of the boundary of the corresponding Euclidean spaces. We also
comment on the thermodynamics of the wormhole spacetimes.Comment: 28 pages, 14 figure
Independent Loop Invariants for 2+1 Gravity
We identify an explicit set of complete and independent Wilson loop
invariants for 2+1 gravity on a three-manifold , with
a compact oriented Riemann surface of arbitrary genus . In the
derivation we make use of a global cross section of the -principal
bundle over Teichm\"uller space given in terms of Fenchel-Nielsen coordinates.Comment: 11pp, 2 figures (postscript, compressed and uu-encoded), TeX,
Pennsylvania State University, CGPG-94/7-
Thurston's pullback map on the augmented Teichm\"uller space and applications
Let be a postcritically finite branched self-cover of a 2-dimensional
topological sphere. Such a map induces an analytic self-map of a
finite-dimensional Teichm\"uller space. We prove that this map extends
continuously to the augmented Teichm\"uller space and give an explicit
construction for this extension. This allows us to characterize the dynamics of
Thurston's pullback map near invariant strata of the boundary of the augmented
Teichm\"uller space. The resulting classification of invariant boundary strata
is used to prove a conjecture by Pilgrim and to infer further properties of
Thurston's pullback map. Our approach also yields new proofs of Thurston's
theorem and Pilgrim's Canonical Obstruction theorem.Comment: revised version, 28 page
New Loop Representations for 2+1 Gravity
Since the gauge group underlying 2+1-dimensional general relativity is
non-compact, certain difficulties arise in the passage from the connection to
the loop representations. It is shown that these problems can be handled by
appropriately choosing the measure that features in the definition of the loop
transform. Thus, ``old-fashioned'' loop representations - based on ordinary
loops - do exist. In the case when the spatial topology is that of a two-torus,
these can be constructed explicitly; {\it all} quantum states can be
represented as functions of (homotopy classes of) loops and the scalar product
and the action of the basic observables can be given directly in terms of
loops.Comment: 28pp, 1 figure (postscript, compressed and uuencoded), TeX,
Pennsylvania State University, CGPG-94/5-
Harmonic maps from degenerating Riemann surfaces
We study harmonic maps from degenerating Riemann surfaces with uniformly
bounded energy and show the so-called generalized energy identity. We find
conditions that are both necessary and sufficient for the compactness in
and modulo bubbles of sequences of such maps.Comment: 27 page
On the appearance of Eisenstein series through degeneration
Let be a Fuchsian group of the first kind acting on the hyperbolic
upper half plane , and let be the
associated finite volume hyperbolic Riemann surface. If is parabolic,
there is an associated (parabolic) Eisenstein series, which, by now, is a
classical part of mathematical literature. If is hyperbolic, then,
following ideas due to Kudla-Millson, there is a corresponding hyperbolic
Eisenstein series. In this article, we study the limiting behavior of parabolic
and hyperbolic Eisenstein series on a degenerating family of finite volume
hyperbolic Riemann surfaces. In particular, we prove the following result. If
corresponds to a degenerating hyperbolic element, then a
multiple of the associated hyperbolic Eisenstein series converges to parabolic
Eisenstein series on the limit surface.Comment: 15 pages, 2 figures. This paper has been accepted for publication in
Commentarii Mathematici Helvetic
Multiple impact therapy : evaluation and design for future study
The theoretical underpinnings of Washington County Children\u27s Services Division (CSD) Immediate Conflict-Resolution Family Treatment Program include the systems theory of family therapy with a focus on communication and roles. One of the many approaches to helping families in crisis, it incorporates theories regarding assessment of and intervention in families in crisis. Finally, while it draws upon several different approaches to family therapy, the Washington County program is most closely related to Multiple Impact Therapy (MIT). Thus, a review of relevant literature must address portions of the above enumerated theories that illuminate the thinking behind the Immediate Conflict- Resolution Family Treatment Program. While each of the four components of the literature review (systems theory, family crisis theory, assessment of families in crisis, and Multiple Impact Therapy) represents a topic area of breadth and complexity, the aspects of each topic area which seem most relevant to Washington County\u27s MIT project have been reviewed
Prevalence and Characteristics of School Services for High School Students with Attention-Deficit/Hyperactivity Disorder
This study examines the prevalence and characteristics of services reported by school staff for 543 high school students participating in the 8 year follow-up of the multi-site Multimodal Treatment study of ADHD (MTA). Overall, 51.6% of students with a history of attention-deficit/hyperactivity disorder (ADHD) were receiving services through an Individualized Educational Plan (IEP) or a 504 plan, a rate higher than expected for this age group. Less than 5% of these had 504 plans; 35.5% attended special education classes. Very few services (except tutoring) were provided outside of an IEP or 504 plan. Almost all students with services received some type of academic intervention, whereas only half received any behavioral support or learning strategy. Less than one-fourth of interventions appear to be evidence-based. Students receiving services showed greater academic and behavioral needs than those not receiving services. Services varied based upon type of school, with the greatest number of interventions provided to students attending schools that only serve those with disabilities. Original MTA treatment randomization was unrelated to services, but cumulative stimulant medication and greater severity predicted more service receipt. Results highlight a need for accommodations with greater evidence of efficacy and for increased services for students who develop academic difficulties in high school
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