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

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

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