485 research outputs found
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
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
Dirac spinor fields in the teleparallel gravity: comment on "Metric-affine approach to teleparallel gravity"
We show that the coupling of a Dirac spinor field with the gravitational
field in the teleparallel equivalent of general relativity is consistent. For
an arbitrary SO(3,1) connection there are two possibilities for the coupling of
the spinor field with the gravitational field. The problems of consistency
raised by Y. N. Obukhov and J. G. Pereira in the paper {\it Metric-affine
approach to teleparallel gravity} [gr-qc/0212080] take place only in the
framework of one particular coupling. By adopting an alternative coupling the
consistency problem disappears.Comment: 8 pages, Latex file, no figures, to appear in the Phys. Rev. D as a
Commen
Time to revise our dialogue : how flat is the paediatric flatfoot?
A recent systematic review of measures of foot development used the medial longitudinal arch profile as its primary indicator of development. A comparative analysis of existing studies was undertaken. This work confirmed changes with arch profile were age-dependent, although the age at which foot development ceased remains unknown. This work also highlighted the abundance of clinical measures used in existing research and outlined the challenges with drawing consensus from available data. There is a clear need to move this debate forward and, to do so, it is essential that scientific and clinical communities unite. It is time to abandon ill-defined measures of foot position, look beyond the medial longitudinal arch as a sole parameter of foot development and re-focus our perspective(s) on the paediatric foot in order to make advances with clinical practice and research
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.
Black Hole Solutions of Kaluza-Klein Supergravity Theories and String Theory
We find U(1)_{E} \times U(1)_{M} non-extremal black hole solutions of
6-dimensional Kaluza-Klein supergravity theories. Extremal solutions were found
by Cveti\v{c} and Youm\cite{C-Y}. Multi black hole solutions are also
presented. After electro-magnetic duality transformation is performed, these
multi black hole solutions are mapped into the the exact solutions found by
Horowitz and Tseytlin\cite{H-T} in 5-dimensional string theory compactified
into 4-dimensions. The massless fields of this theory can be embedded into the
heterotic string theory compactified on a 6-torus. Rotating black hole
solutions can be read off those of the heterotic string theory found by
Sen\cite{Sen3}.Comment: 23 pages text(latex), a figure upon reques
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