9,668 research outputs found
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
Apollo experience report the command and service module milestone review process
The sequence of the command and service module milestone review process is given, and the Customer Acceptance Readiness Review and Flight Readiness Review plans are presented. Contents of the System Summary Acceptance Documents for the two formal spacecraft reviews are detailed, and supplemental data required for presentation to the review boards are listed. Typical forms, correspondence, supporting documentation, and minutes of a board meeting are included
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.
Freire re-viewed
The work of Paulo Freire is associated with themes of oppression and liberation, and his critical pedagogy is visionary in its attempts to bring about social transformation. Freire has created a theory of education that embeds these issues within social relations that center around both ideological and material domination. In this review essay, Sue Jackson explores three books: Freire’s final work Pedagogy of Indignation; Cesar Augusto Rossatto’s Engaging Paulo Freire’s Pedagogy of Possibility, which attempts to engage Freire’s pedagogy of possibility; and C.A. Bowers and Frederique Apffel-Marglin’s edited collection Re-thinking Freire, which asks readers to reconsider Freire’s work in light of globalization and environmental crises. Jackson questions the extent to which Freire’s pedagogical approaches are useful to educators as well as to “the oppressed,” and whether challenges to re-think Freire can lead to new kinds of critical pedagogies
Hyperbolicity and Constrained Evolution in Linearized Gravity
Solving the 4-d Einstein equations as evolution in time requires solving
equations of two types: the four elliptic initial data (constraint) equations,
followed by the six second order evolution equations. Analytically the
constraint equations remain solved under the action of the evolution, and one
approach is to simply monitor them ({\it unconstrained} evolution). Since
computational solution of differential equations introduces almost inevitable
errors, it is clearly "more correct" to introduce a scheme which actively
maintains the constraints by solution ({\it constrained} evolution). This has
shown promise in computational settings, but the analysis of the resulting
mixed elliptic hyperbolic method has not been completely carried out. We
present such an analysis for one method of constrained evolution, applied to a
simple vacuum system, linearized gravitational waves.
We begin with a study of the hyperbolicity of the unconstrained Einstein
equations. (Because the study of hyperbolicity deals only with the highest
derivative order in the equations, linearization loses no essential details.)
We then give explicit analytical construction of the effect of initial data
setting and constrained evolution for linearized gravitational waves. While
this is clearly a toy model with regard to constrained evolution, certain
interesting features are found which have relevance to the full nonlinear
Einstein equations.Comment: 18 page
A Liquid Model Analogue for Black Hole Thermodynamics
We are able to characterize a 2--dimensional classical fluid sharing some of
the same thermodynamic state functions as the Schwarzschild black hole. This
phenomenological correspondence between black holes and fluids is established
by means of the model liquid's pair-correlation function and the two-body
atomic interaction potential. These latter two functions are calculated exactly
in terms of the black hole internal (quasilocal) energy and the isothermal
compressibility. We find the existence of a ``screening" like effect for the
components of the liquid.Comment: 20 pages and 6 Encapsulated PostScript figure
Simulating merging binary black holes with nearly extremal spins
Astrophysically realistic black holes may have spins that are nearly extremal
(i.e., close to 1 in dimensionless units). Numerical simulations of binary
black holes are important tools both for calibrating analytical templates for
gravitational-wave detection and for exploring the nonlinear dynamics of curved
spacetime. However, all previous simulations of binary-black-hole inspiral,
merger, and ringdown have been limited by an apparently insurmountable barrier:
the merging holes' spins could not exceed 0.93, which is still a long way from
the maximum possible value in terms of the physical effects of the spin. In
this paper, we surpass this limit for the first time, opening the way to
explore numerically the behavior of merging, nearly extremal black holes.
Specifically, using an improved initial-data method suitable for binary black
holes with nearly extremal spins, we simulate the inspiral (through 12.5
orbits), merger and ringdown of two equal-mass black holes with equal spins of
magnitude 0.95 antialigned with the orbital angular momentum.Comment: 4 pages, 2 figures, updated with version accepted for publication in
Phys. Rev. D, removed a plot that was incorrectly included at the end of the
article in version v
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
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