2,581 research outputs found
Development of integrated programs for Aerospace-vehicle Design (IPAD): Product program management systems
The Integrated Programs for Aerospace Vehicle Design (IPAD) is a computing system to support company-wide design information processing. This document presents a brief description of the management system used to direct and control a product-oriented program. This document, together with the reference design process (CR 2981) and the manufacture interactions with the design process (CR 2982), comprises the reference information that forms the basis for specifying IPAD system requirements
Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics
We show that sets of conformal data on closed manifolds with the metric in
the positive or zero Yamabe class, and with the gradient of the mean curvature
function sufficiently small, are mapped to solutions of the Einstein constraint
equations. This result extends previous work which required the conformal
metric to be in the negative Yamabe class, and required the mean curvature
function to be nonzero.Comment: 15 page
Oscillatory approach to the singularity in vacuum symmetric spacetimes
A combination of qualitative analysis and numerical study indicates that
vacuum symmetric spacetimes are, generically, oscillatory.Comment: 2 pages submitted to the Ninth Marcel Grossmann Proceedings; v2, "all
known cases" changed to "various known cases" in the first paragrap
A model problem for conformal parameterizations of the Einstein constraint equations
We investigate the possibility that the conformal and conformal thin sandwich
(CTS) methods can be used to parameterize the set of solutions of the vacuum
Einstein constraint equations. To this end we develop a model problem obtained
by taking the quotient of certain symmetric data on conformally flat tori.
Specializing the model problem to a three-parameter family of conformal data we
observe a number of new phenomena for the conformal and CTS methods. Within
this family, we obtain a general existence theorem so long as the mean
curvature does not change sign. When the mean curvature changes sign, we find
that for certain data solutions exist if and only if the transverse-traceless
tensor is sufficiently small. When such solutions exist, there are generically
more than one. Moreover, the theory for mean curvatures changing sign is shown
to be extremely sensitive with respect to the value of a coupling constant in
the Einstein constraint equations.Comment: 40 pages, 4 figure
Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations
We describe how the iterative technique used by Isenberg and Moncrief to
verify the existence of large sets of non constant mean curvature solutions of
the Einstein constraints on closed manifolds can be adapted to verify the
existence of large sets of asymptotically hyperbolic non constant mean
curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure
A rigidity theorem for nonvacuum initial data
In this note we prove a theorem on non-vacuum initial data for general
relativity. The result presents a ``rigidity phenomenon'' for the extrinsic
curvature, caused by the non-positive scalar curvature.
More precisely, we state that in the case of asymptotically flat non-vacuum
initial data if the metric has everywhere non-positive scalar curvature then
the extrinsic curvature cannot be compactly supported.Comment: This is an extended and published version: LaTex, 10 pages, no
figure
The constraint equations for the Einstein-scalar field system on compact manifolds
We study the constraint equations for the Einstein-scalar field system on
compact manifolds. Using the conformal method we reformulate these equations as
a determined system of nonlinear partial differential equations. By introducing
a new conformal invariant, which is sensitive to the presence of the initial
data for the scalar field, we are able to divide the set of free conformal data
into subclasses depending on the possible signs for the coefficients of terms
in the resulting Einstein-scalar field Lichnerowicz equation. For many of these
subclasses we determine whether or not a solution exists. In contrast to other
well studied field theories, there are certain cases, depending on the mean
curvature and the potential of the scalar field, for which we are unable to
resolve the question of existence of a solution. We consider this system in
such generality so as to include the vacuum constraint equations with an
arbitrary cosmological constant, the Yamabe equation and even (all cases of)
the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum
Gravit
Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations
We show that asymptotically hyperbolic solutions of the Einstein constraint
equations with constant mean curvature can be glued in such a way that their
asymptotic regions are connected.Comment: 37 pages; 2 figure
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
Ricci flows, wormholes and critical phenomena
We study the evolution of wormhole geometries under Ricci flow using
numerical methods. Depending on values of initial data parameters, wormhole
throats either pinch off or evolve to a monotonically growing state. The
transition between these two behaviors exhibits a from of critical phenomena
reminiscent of that observed in gravitational collapse. Similar results are
obtained for initial data that describe space bubbles attached to
asymptotically flat regions. Our numerical methods are applicable to
"matter-coupled" Ricci flows derived from conformal invariance in string
theory.Comment: 8 pages, 5 figures. References added and minor changes to match
version accepted by CQG as a fast track communicatio
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