Oscillatory approach to the singularity in vacuum T2T^2 symmetric spacetimes

A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ 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

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

General Relativity and Gravitation: A Centennial Perspective

To commemorate the 100th anniversary of general relativity, the International Society on General Relativity and Gravitation (ISGRG) commissioned a Centennial Volume, edited by the authors of this article. We jointly wrote introductions to the four Parts of the Volume which are collected here. Our goal is to provide a bird's eye view of the advances that have been made especially during the last 35 years, i.e., since the publication of volumes commemorating Einstein's 100th birthday. The article also serves as a brief preview of the 12 invited chapters that contain in-depth reviews of these advances. The volume will be published by Cambridge University Press and released in June 2015 at a Centennial conference sponsored by ISGRG and the Topical Group of Gravitation of the American Physical Society.Comment: 37 page

Waveless Approximation Theories of Gravity

The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability -- are associated with the presence of gravitational waves. We have developed a number of ``waveless approximation theories'' (WAT) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory

A Conceptual Learner-Centered e-Learning Framework

e-Learning has increased rapidly in higher education. Most online education attempts to mirror the traditional face-to-face (FtF) classroom with less than favourable results. This paper proposes a conceptual e-learning framework based on andragogy theory, transformative learning theory, and media synchronicity theory. The conceptual e-learning framework supports the self-directed learning. e-learning based on this framework has the potential to out-perform not only current learning management systems such as Blackboard, but also traditional FtF learning for adult education and with different and better outcomes. Results of early testing of the concept showed increased learner’s online activity, innovation, and creativity

Andragogically Building a Doctor of Andragogy Program

Developing and implementing a Doctor of Andragogy Program andragogically provides an opportunity to ‘think outside the box’. It requires congruency between talking and action. Is this possible to accomplish? Stay tuned

Canonical Quantization Inside the Schwarzschild Black Hole

We propose a scheme for quantizing a scalar field over the Schwarzschild manifold including the interior of the horizon. On the exterior, the timelike Killing vector and on the horizon the isometry corresponding to restricted Lorentz boosts can be used to enforce the spectral condition. For the interior we appeal to the need for CPT invariance to construct an explicitly positive definite operator which allows identification of positive and negative frequencies. This operator is the translation operator corresponding to the inexorable propagation to smaller radii as expected from the classical metric. We also propose an expression for the propagator in the interior and express it as a mode sum.Comment: 8 pages, LaTex. Title altered. One reference added. A few typos esp. eq.(7),(38) corrected. To appear in Class.Q.Gra