35 research outputs found
Origin of the Immirzi Parameter
Using quadratic spinor techniques we demonstrate that the Immirzi parameter
can be expressed as ratio between scalar and pseudo-scalar contributions in the
theory and can be interpreted as a measure of how Einstein gravity differs from
a generally constructed covariant theory for gravity. This interpretation is
independent of how gravity is quantized. One of the important advantage of
deriving the Immirzi parameter using the quadratic spinor techniques is to
allow the introduction of renormalization scale associated with the Immirzi
parameter through the expectation value of the spinor field upon quantization
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.
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
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
A Quadratic Spinor Lagrangian for General Relativity
We present a new finite action for Einstein gravity in which the Lagrangian
is quadratic in the covariant derivative of a spinor field. Via a new
spinor-curvature identity, it is related to the standard Einstein-Hilbert
Lagrangian by a total differential term. The corresponding Hamiltonian, like
the one associated with the Witten positive energy proof is fully
four-covariant. It defines quasi-local energy-momentum and can be reduced to
the one in our recent positive energy proof. (Fourth Prize, 1994 Gravity
Research Foundation Essay.)Comment: 5 pages (Plain TeX), NCU-GR-94-QSL
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
Scalar Field Cosmology II: Superfluidity, Quantum Turbulence, and Inflation
We generalize the big-bang model in a previous paper by extending the real
vacuum scalar field to a complex vacuum scalar field, within the FLRW
framework. The phase dynamics of the scalar field, which makes the universe a
superfluid, is described in terms of a density of quantized vortex lines, and a
tangle of vortex lines gives rise to quantum turbulence. We propose that all
the matter in the universe was created in the turbulence, through reconnection
of vortex lines, a process necessary for the maintenance of the vortex tangle.
The vortex tangle grows and decays, and its lifetime is the era of inflation.
These ideas are implemented in a set of closed cosmological equations that
describe the cosmic expansion driven by the scalar field on the one hand, and
the vortex-matter dynamics on the other. We show how these two aspects decouple
from each other, due to a vast difference in energy scales. The model is not
valid beyond the inflation era, but the universe remains a superfluid
afterwards. This gives rise to observable effects in the present universe,
including dark matter, galactic voids, non-thermal filaments, and cosmic jets.Comment: 29 pages, 7 figures, published versio
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