8,153 research outputs found
The Initial Value Problem Using Metric and Extrinsic Curvature
The initial value problem is introduced after a thorough review of the
essential geometry. The initial value equations are put into elliptic form
using both conformal transformations and a treatment of the extrinsic curvature
introduced recently. This use of the metric and the extrinsic curvature is
manifestly equivalent to the author's conformal thin sandwich formulation.
Therefore, the reformulation of the constraints as an elliptic system by use of
conformal techniques is complete.Comment: 10 pages, to appear in the Proceedings of the Tenth Marcel Grossmann
Meeting on General Relativit
Application of quasi-homogeneous anisotropic laminates in grid-stiffened panel design
Composite laminates are derived for standard configurations with quasi-homogeneous anisotropic properties, whereby in-plane and out-of-plane stiffness properties are concomitant. Dimensionless parameters, and their relationship to the well-known ply- orientation-dependent lamination parameters, are also developed from which the elements of the extensional and bending stiffness matrices are readily calculated for any fiber/resin properties. The definitive list of laminate configurations for up to 21 plies is presented, together with graphical representations of the lamination parameter design space for standard ply orientations +45, -45, 0 and 90 degrees. Finally, the potential of quasi-homogeneous anisotropic laminates as an optimum design solution for anisogid structures is explored for cases where buckling and strength constraints are both active
Path Integral Over Black Hole Fluctuations
Evaluating a functional integral exactly over a subset of metrics that
represent the quantum fluctuations of the horizon of a black hole, we obtain a
Schroedinger equation in null coordinate time for the key component of the
metric. The equation yields a current that preserves probability if we use the
most natural choice of functional measure. This establishes the existence of
blurred horizons and a thermal atmosphere. It has been argued previously that
the existence of a thermal atmosphere is a direct concomitant of the thermal
radiation of black holes when the temperature of the hole is greater than that
of its larger environment, which we take as zero.Comment: 5 pages, added a couple of clarification
Conformal ``thin sandwich'' data for the initial-value problem of general relativity
The initial-value problem is posed by giving a conformal three-metric on each
of two nearby spacelike hypersurfaces, their proper-time separation up to a
multiplier to be determined, and the mean (extrinsic) curvature of one slice.
The resulting equations have the {\it same} elliptic form as does the
one-hypersurface formulation. The metrical roots of this form are revealed by a
conformal ``thin sandwich'' viewpoint coupled with the transformation
properties of the lapse function.Comment: 7 pages, RevTe
Fixing Einstein's equations
Einstein's equations for general relativity, when viewed as a dynamical
system for evolving initial data, have a serious flaw: they cannot be proven to
be well-posed (except in special coordinates). That is, they do not produce
unique solutions that depend smoothly on the initial data. To remedy this
failing, there has been widespread interest recently in reformulating
Einstein's theory as a hyperbolic system of differential equations. The
physical and geometrical content of the original theory remain unchanged, but
dynamical evolution is made sound. Here we present a new hyperbolic formulation
in terms of , , and \bGam_{kij} that is strikingly close to
the space-plus-time (``3+1'') form of Einstein's original equations. Indeed,
the familiarity of its constituents make the existence of this formulation all
the more unexpected. This is the most economical first-order symmetrizable
hyperbolic formulation presently known to us that has only physical
characteristic speeds, either zero or the speed of light, for all (non-matter)
variables. This system clarifies the relationships between Einstein's original
equations and the Einstein-Ricci and Frittelli-Reula hyperbolic formulations of
general relativity and establishes links to other hyperbolic formulations.Comment: 8 pages, revte
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