Existence of CMC Cauchy surfaces and spacetime splitting

In this paper, we review results on the existence (and nonexistence) of constant mean curvature spacelike hypersurfaces in the cosmological setting, and discuss the connection to the spacetime splittng problem. It is a pleasure to dedicate this paper to Robert Bartnik, who has made fundamental contributions to this area.Comment: 16 page

Introduction to the Neoclassical Interpretation: Quantum Steampunk

In a previous paper we outlined a series of historical touchpoints between classical aether theories and modern theoretical physics which showed a shared conceptual lineage for the modern tools and methods of the most common interpretations and fluid based “Hydrodynamic” treatments of an electromagnetic medium. It was proposed that, though the weight of modern experimentation leaves an extremely narrow and convoluted window for even a reconceptualization of a medium, all of modern physics recognizes a plethora of behaviors and attributes for free space and these physics are interchangeable with modern methods for treating superfluid-like continuums. Thus the mathematical equivalence of the methods do not comprise alternative physics but an alternative interpretation of the same physics. Though many individual components describing a “neo-aether” or “quintessence” are available, an overarching structural outline of how these tools can work together to provide an alternative working overview of modern physics has remained undefined. This paper will propose a set of introductory concepts in the first outline of a toy model which will later connect the alternative tools and conceptualizations with their modern counterparts. This introductory paper provides the simpler “100-miles out” overview of the whole of physics from this perspective, in an easily comprehensible, familiar and intuitive, informal dialog fashion. While this paper grants the largest and loosest introductory overview, subsequent papers in this series will address the finite connections between modern physics and this hydrodynamic view

Maximum Principles for Null Hypersurfaces and Null Splitting Theorems

A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum (Ricci flat) spacetime which contains a null line is isometric to Minkowski space.Comment: 26 pages, latex2

An introduction to local Black Hole horizons in the 3+1 approach to General Relativity

We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an "a priori" ingredient in certain formulations of Einstein equations and as an "a posteriori" tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the "rigidity" properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.Comment: 37 pages, 5 figures. Notes prepared for the course at the 2011 Shanghai Asia-Pacific School and Workshop on Gravitation (Shanghai Normal University, February 10-14, 2011