6,410 research outputs found
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
Excision boundary conditions for black hole initial data
We define and extensively test a set of boundary conditions that can be
applied at black hole excision surfaces when the Hamiltonian and momentum
constraints of general relativity are solved within the conformal thin-sandwich
formalism. These boundary conditions have been designed to result in black
holes that are in quasiequilibrium and are completely general in the sense that
they can be applied with any conformal three-geometry and slicing condition.
Furthermore, we show that they retain precisely the freedom to specify an
arbitrary spin on each black hole. Interestingly, we have been unable to find a
boundary condition on the lapse that can be derived from a quasiequilibrium
condition. Rather, we find evidence that the lapse boundary condition is part
of the initial temporal gauge choice. To test these boundary conditions, we
have extensively explored the case of a single black hole and the case of a
binary system of equal-mass black holes, including the computation of
quasi-circular orbits and the determination of the inner-most stable circular
orbit. Our tests show that the boundary conditions work well.Comment: 23 pages, 23 figures, revtex4, corrected typos, added reference,
minor content changes including additional post-Newtonian comparison. Version
accepted by PR
Uniqueness and Non-uniqueness in the Einstein Constraints
The conformal thin sandwich (CTS) equations are a set of four of the Einstein
equations, which generalize the Laplace-Poisson equation of Newton's theory. We
examine numerically solutions of the CTS equations describing perturbed
Minkowski space, and find only one solution. However, we find {\em two}
distinct solutions, one even containing a black hole, when the lapse is
determined by a fifth elliptic equation through specification of the mean
curvature. While the relationship of the two systems and their solutions is a
fundamental property of general relativity, this fairly simple example of an
elliptic system with non-unique solutions is also of broader interest.Comment: 4 pages, 4 figures; abstract and introduction rewritte
Dynamical evolution of unstable self-gravitating scalar solitons
Recently, static and spherically symmetric configurations of globally regular
self-gravitating scalar solitons were found. These configurations are unstable
with respect to radial linear perturbations. In this paper we study the
dynamical evolution of such configurations and show that, depending on the sign
of the initial perturbation, the solitons either collapse to a Schwarzschild
black hole or else ``explode'' into an outward moving domain wall.Comment: 11 pages, 16 figures, submitted to Phys. Rev.
Scale-invariant gravity: Spacetime recovered
The configuration space of general relativity is superspace - the space of
all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued
that the configuration space for gravity should be conformal superspace - the
space of all Riemannian 3-metrics modulo diffeomorphisms and conformal
transformations. Recently a manifestly 3-dimensional theory was constructed
with conformal superspace as the configuration space. Here a fully
4-dimensional action is constructed so as to be invariant under conformal
transformations of the 4-metric using general relativity as a guide. This
action is then decomposed to a (3+1)-dimensional form and from this to its
Jacobi form. The surprising thing is that the new theory turns out to be
precisely the original 3-dimensional theory. The physical data is identified
and used to find the physical representation of the theory. In this
representation the theory is extremely similar to general relativity. The
clarity of the 4-dimensional picture should prove very useful for comparing the
theory with those aspects of general relativity which are usually treated in
the 4-dimensional framework.Comment: Replaced with final version: minor changes to tex
Constraint Damping in First-Order Evolution Systems for Numerical Relativity
A new constraint suppressing formulation of the Einstein evolution equations
is presented, generalizing the five-parameter first-order system due to Kidder,
Scheel and Teukolsky (KST). The auxiliary fields, introduced to make the KST
system first-order, are given modified evolution equations designed to drive
constraint violations toward zero. The algebraic structure of the new system is
investigated, showing that the modifications preserve the hyperbolicity of the
fundamental and constraint evolution equations. The evolution of the
constraints for pertubations of flat spacetime is completely analyzed, and all
finite-wavelength constraint modes are shown to decay exponentially when
certain adjustable parameters satisfy appropriate inequalities. Numerical
simulations of a single Schwarzschild black hole are presented, demonstrating
the effectiveness of the new constraint-damping modifications.Comment: 11 pages, 5 figure
Positivity of Entropy in the Semi-Classical Theory of Black Holes and Radiation
Quantum stress-energy tensors of fields renormalized on a Schwarzschild
background violate the classical energy conditions near the black hole.
Nevertheless, the associated equilibrium thermodynamical entropy by
which such fields augment the usual black hole entropy is found to be positive.
More precisely, the derivative of with respect to radius, at fixed
black hole mass, is found to vanish at the horizon for {\it all} regular
renormalized stress-energy quantum tensors. For the cases of conformal scalar
fields and U(1) gauge fields, the corresponding second derivative is positive,
indicating that has a local minimum there. Explicit calculation
shows that indeed increases monotonically for increasing radius and
is positive. (The same conclusions hold for a massless spin 1/2 field, but the
accuracy of the stress-energy tensor we employ has not been confirmed, in
contrast to the scalar and vector cases). None of these results would hold if
the back-reaction of the radiation on the spacetime geometry were ignored;
consequently, one must regard as arising from both the radiation
fields and their effects on the gravitational field. The back-reaction, no
matter how "small",Comment: 19 pages, RevTe
No-go theorem for bimetric gravity with positive and negative mass
We argue that the most conservative geometric extension of Einstein gravity
describing both positive and negative mass sources and observers is bimetric
gravity and contains two copies of standard model matter which interact only
gravitationally. Matter fields related to one of the metrics then appear dark
from the point of view of an observer defined by the other metric, and so may
provide a potential explanation for the dark universe. In this framework we
consider the most general form of linearized field equations compatible with
physically and mathematically well-motivated assumptions. Using gauge-invariant
linear perturbation theory, we prove a no-go theorem ruling out all bimetric
gravity theories that, in the Newtonian limit, lead to precisely opposite
forces on positive and negative test masses.Comment: 19 pages, no figures, journal versio
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