Ashtekar's New Variables and Positive Energy

We discuss earlier unsuccessful attempts to formulate a positive gravitational energy proof in terms of the New Variables of Ashtekar. We also point out the difficulties of a Witten spinor type proof. We then use the special orthonormal frame gauge conditions to obtain a locally positive expression for the New Variables Hamiltonian and thereby a ``localization'' of gravitational energy as well as a positive energy proof.Comment: 12 pages Plain Te

The quadratic spinor Lagrangian is equivalent to the teleparallel theory

The quadratic spinor Lagrangian is shown to be equivalent to the teleparallel / tetrad representation of Einstein's theory. An important consequence is that the energy-momentum density obtained from this quadratic spinor Lagrangian is essentially the same as the ``tensor'' proposed by Moller in 1961.Comment: 10 pages, RevTe

The effect of aging, obesity and diabetes on foot health and its association with current and future footwear technologies

Changes in foot health trends are beginning to demand significant changes to foot health provision globally, for which appropriate provision to retail and health services is key. With the right input to innovation and design, footwear can help keep us fit and active and contribute to our overall wellbeing, creating exciting opportunities for the footwear market. Likewise, the development of orthotic materials, designs and manufacturing processes is enabling more complex solutions to equally complex developing foot conditions. There are three key issues driving the demand for specific footcare; the global increase in the number of people with diabetes, those who are obese and the fact we are all living longer. The populations of diabetic, elderly and obese adults require specific footcare solutions to meet the specific characteristics of their foot health issues such as wider-fit footwear and pressure relieving orthotic materials. Characteristics of these populations' feet relating to their morphology, tissue characteristics, vascular supply and sensation impact on their requirements from footwear. Additional characteristics relating to their overall health such as excess mass and instability additionally impact on the wear on the loading of the footwear and design features which may be beneficial

Quasi-local Energy for Spherically Symmetric Spacetimes

We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface and extremize the energy. This can be done in two ways, which we call programs I (without constraint) and II (with additional constraints). On the other hand, we match the orthonormal 4-frames of the dynamic and the reference spacetimes. Then, if we further specify the observer by requiring the reference displacement to be the timelike Killing vector of the reference, the result is the same as program I, and the energy can be positive, zero, or even negative. If, instead, we require that the Lie derivatives of the two-area along the displacement vector in both the dynamic and reference spacetimes to be the same, the result is the same as program II, and it satisfies the usual criteria: the energies are non-negative and vanish only for Minkowski (or anti-de Sitter) spacetime.Comment: 16 pages, no figure

Quasi-local energy for cosmological models

First we briefly review our covariant Hamiltonian approach to quasi-local energy, noting that the Hamiltonian-boundary-term quasi-local energy expressions depend on the chosen boundary conditions and reference configuration. Then we present the quasi-local energy values resulting from the formalism applied to homogeneous Bianchi cosmologies. Finally we consider the quasi-local energies of the FRW cosmologies. Our results do not agree with certain widely accepted quasi-local criteria.Comment: Contributed to International Symposium on Cosmology and Particle Astrophysics (CosPA 2006), Taipei, Taiwan, 15-17 Nov 200

The Hamiltonian boundary term and quasi-local energy flux

The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasi-local values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasi-local energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasi-local energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasi-local expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant.Comment: 12 pages, no figures, revtex

Quasi-local energy-momentum and energy flux at null infinity

The null infinity limit of the gravitational energy-momentum and energy flux determined by the covariant Hamiltonian quasi-local expressions is evaluated using the NP spin coefficients. The reference contribution is considered by three different embedding approaches. All of them give the expected Bondi energy and energy flux.Comment: 14 pages, accepted by Phys.Rev.

Gravitational energy from a combination of a tetrad expression and Einstein's pseudotensor

The energy-momentum for a gravitating system can be considered by the tetard teleparalle gauge current in orthonormal frames. Whereas the Einstein pseudotensor used holonomic frames. Tetrad expression itself gives a better result for gravitational energy than Einstein's. Inspired by an idea of Deser, we found a gravitational energy expression which enjoys the positive energy property by combining the tetrad expression and the Einstein pseudotensor, i.e., the connection coefficient has a form appropriate to a suitable intermediate between orthonormal and holonomic frames.Comment: 5 page