Stationary untrapped boundary conditions in general relativity

A class of boundary conditions for canonical general relativity are proposed and studied at the quasi-local level. It is shown that for untrapped or marginal surfaces, fixing the area element on the 2-surface (rather than the induced 2-metric) and the angular momentum surface density is enough to have a functionally differentiable Hamiltonian, thus providing definition of conserved quantities for the quasi-local regions. If on the boundary the evolution vector normal to the 2-surface is chosen to be proportional to the dual expansion vector, we obtain a generalization of the Hawking energy associated with a generalized Kodama vector. This vector plays the role for the stationary untrapped boundary conditions which the stationary Killing vector plays for stationary black holes. When the dual expansion vector is null, the boundary conditions reduce to the ones given by the non-expanding horizons and the null trapping horizons.Comment: 11 pages, improved discussion section, a reference added, accepted for publication in Classical and Quantum Gravit

Quasi-Local Energy Flux of Spacetime Perturbation

A general expression for quasi-local energy flux for spacetime perturbation is derived from covariant Hamiltonian formulation using functional differentiability and symplectic structure invariance, which is independent of the choice of the canonical variables and the possible boundary terms one initially puts into the Lagrangian in the diffeomorphism invariant theories. The energy flux expression depends on a displacement vector field and the 2-surface under consideration. We apply and test the expression in Vaidya spacetime. At null infinity the expression leads to the Bondi type energy flux obtained by Lindquist, Schwartz and Misner. On dynamical horizons with a particular choice of the displacement vector, it gives the area balance law obtained by Ashtekar and Krishnan.Comment: 8 pages, added appendix, version to appear in Phys. Rev.

Some Spinor-Curvature Identities

We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the curvature plus an exact differential. Certain special cases in 3 and 4 dimensions which have been or could be used in applications to General Relativity are noted.Comment: 5 pages Plain TeX, NCU-GR-93-SSC

Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions

We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying ``energy-momentum'' vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the resulting Dirichlet and Neumann vectors for topologically spherical 2-surfaces in Minkowski spacetime, spherically symmetric spacetimes, and stationary axisymmetric spacetimes. Moreover, we show the relation between these vectors and the ADM energy-momentum vector for a 2-surface taken in a limit to be spatial infinity in asymptotically flat spacetimes. We also discuss the geometrical properties of the Dirichlet and Neumann vectors and obtain several striking results relating these vectors to the mean curvature and normal curvature connection of the 2-surface. Most significantly, the part of the Dirichlet vector normal to the 2-surface depends only the spacetime metric at this surface and thereby defines a geometrical normal vector field on the 2-surface. Properties and examples of this normal vector are discussed.Comment: 46 pages; minor errata corrected in Eqs. (3.15), (3.24), (4.37) and in discussion of examples in sections IV B,

The effects of peripheral and central high insulin on brain insulin signaling and amyloid-β in young and old APP/PS1 mice

Hyperinsulinemia is a risk factor for late-onset Alzheimer's disease (AD). In vitro experiments describe potential connections between insulin, insulin signaling, and amyloid-β (Aβ), but in vivo experiments are needed to validate these relationships under physiological conditions. First, we performed hyperinsulinemic-euglycemic clamps with concurrent hippocampal microdialysis in young, awake, behaving APP(swe)/PS1(dE9) transgenic mice. Both a postprandial and supraphysiological insulin clamp significantly increased interstitial fluid (ISF) and plasma Aβ compared with controls. We could detect no increase in brain, ISF, or CSF insulin or brain insulin signaling in response to peripheral hyperinsulinemia, despite detecting increased signaling in the muscle. Next, we delivered insulin directly into the hippocampus of young APP/PS1 mice via reverse microdialysis. Brain tissue insulin and insulin signaling was dose-dependently increased, but ISF Aβ was unchanged by central insulin administration. Finally, to determine whether peripheral and central high insulin has differential effects in the presence of significant amyloid pathology, we repeated these experiments in older APP/PS1 mice with significant amyloid plaque burden. Postprandial insulin clamps increased ISF and plasma Aβ, whereas direct delivery of insulin to the hippocampus significantly increased tissue insulin and insulin signaling, with no effect on Aβ in old mice. These results suggest that the brain is still responsive to insulin in the presence of amyloid pathology but increased insulin signaling does not acutely modulate Aβ in vivo before or after the onset of amyloid pathology. Peripheral hyperinsulinemia modestly increases ISF and plasma Aβ in young and old mice, independent of neuronal insulin signaling. SIGNIFICANCE STATEMENT The transportation of insulin from blood to brain is a saturable process relevant to understanding the link between hyperinsulinemia and AD. In vitro experiments have found direct connections between high insulin and extracellular Aβ, but these mechanisms presume that peripheral high insulin elevates brain insulin significantly. We found that physiological hyperinsulinemia in awake, behaving mice does not increase CNS insulin to an appreciable level yet modestly increases extracellular Aβ. We also found that the brain of aged APP/PS1 mice was not insulin resistant, contrary to the current state of the literature. These results further elucidate the relationship between insulin, the brain, and AD and its conflicting roles as both a risk factor and potential treatment

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 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

Investment Opportunities Forecasting: Extending the Grammar of a GP-based Tool

In this paper we present a new version of a GP financial forecasting tool, called EDDIE 8. The novelty of this version is that it allows the GP to search in the space of indicators, instead of using pre-specified ones. We compare EDDIE 8 with its predecessor, EDDIE 7, and find that new and improved solutions can be found. Analysis also shows that, on average, EDDIE 8's best tree performs better than the one of EDDIE 7. The above allows us to characterize EDDIE 8 as a valuable forecasting tool

Supply chain strategies as drivers of financial performance in liquefied natural gas networks

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