164 research outputs found
Angular momentum of isolated systems
Penrose's twistorial approach to the definition of angular momentum at null
infinity is developed so that angular momenta at different cuts can be
meaningfully compared. This is done by showing that the twistor spaces
associated with different cuts of scri can be identified as manifolds (but not
as vector spaces). The result is a well-defined, Bondi-Metzner-Sachs-invariant
notion of angular momentum in a radiating space-time; the difficulties and
ambiguities previously encountered are attached to attempts to express this in
special-relativistic terms, and in particular to attempts to identify a single
Minkowski space of origins. Unlike the special-relativistic case, the angular
momentum cannot be represented by a purely j=1 quantity M_{ab}, but has
higher-j contributions as well. Applying standard kinematic prescriptions,
these higher-j contributions are shown to correspond precisely to the shear.
Thus it appears that shear and angular momentum should be regarded as different
aspects of a single unified concept.Comment: 23 pages, to appear in GR
Four Dimensional Integrable Theories
There exist many four dimensional integrable theories. They include self-dual
gauge and gravity theories, all their extended supersymmetric generalisations,
as well the full (non-self-dual) N=3 super Yang-Mills equations. We review the
harmonic space formulation of the twistor transform for these theories which
yields a method of producing explicit connections and metrics. This formulation
uses the concept of harmonic space analyticity which is closely related to that
of quaternionic analyticity. (Talk by V. Ogievetsky at the G\"ursey Memorial
Conference I, Istanbul, June 1994)Comment: 11 pages, late
A comment on positive mass for scalar field sources
We use a transformation due to Bekenstein to relate the ADM and Bondi masses
of asymptotically-flat solutions of the Einstein equations with, respectively,
scalar sources and conformal-scalar sources. Although the conformal-scalar
energy-momentum tensor does not satisfy the Dominant Energy Condition one may,
by this means, still conclude that the ADM mass is positive.Comment: 6 page
Complex Kerr Geometry and Nonstationary Kerr Solutions
In the frame of the Kerr-Schild approach, we consider the complex structure
of Kerr geometry which is determined by a complex world line of a complex
source. The real Kerr geometry is represented as a real slice of this complex
structure. The Kerr geometry is generalized to the nonstationary case when the
current geometry is determined by a retarded time and is defined by a
retarded-time construction via a given complex world line of source. A general
exact solution corresponding to arbitrary motion of a spinning source is
obtained. The acceleration of the source is accompanied by a lightlike
radiation along the principal null congruence. It generalizes to the rotating
case the known Kinnersley class of "photon rocket" solutions.Comment: v.3, revtex, 16 pages, one eps-figure, final version (to appear in
PRD), added the relation to twistors and algorithm of numerical computations,
English is correcte
Continuous image distortion by astrophysical thick lenses
Image distortion due to weak gravitational lensing is examined using a
non-perturbative method of integrating the geodesic deviation and optical
scalar equations along the null geodesics connecting the observer to a distant
source. The method we develop continuously changes the shape of the pencil of
rays from the source to the observer with no reference to lens planes in
astrophysically relevant scenarios. We compare the projected area and the ratio
of semi-major to semi-minor axes of the observed elliptical image shape for
circular sources from the continuous, thick-lens method with the commonly
assumed thin-lens approximation. We find that for truncated singular isothermal
sphere and NFW models of realistic galaxy clusters, the commonly used thin-lens
approximation is accurate to better than 1 part in 10^4 in predicting the image
area and axes ratios. For asymmetric thick lenses consisting of two massive
clusters separated along the line of sight in redshift up to \Delta z = 0.2, we
find that modeling the image distortion as two clusters in a single lens plane
does not produce relative errors in image area or axes ratio more than 0.5%Comment: accepted to GR
An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics
A general method for deriving closed reduced models of Hamiltonian dynamical
systems is developed using techniques from optimization and statistical
estimation. As in standard projection operator methods, a set of resolved
variables is selected to capture the slow, macroscopic behavior of the system,
and the family of quasi-equilibrium probability densities on phase space
corresponding to these resolved variables is employed as a statistical model.
The macroscopic dynamics of the mean resolved variables is determined by
optimizing over paths of these probability densities. Specifically, a cost
function is introduced that quantifies the lack-of-fit of such paths to the
underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of
the residual that results from submitting a path of trial densities to the
Liouville equation. The evolution of the macrostate is estimated by minimizing
the time integral of the cost function. The value function for this
optimization satisfies the associated Hamilton-Jacobi equation, and it
determines the optimal relation between the statistical parameters and the
irreversible fluxes of the resolved variables, thereby closing the reduced
dynamics. The resulting equations for the macroscopic variables have the
generic form of governing equations for nonequilibrium thermodynamics, and they
furnish a rational extension of the classical equations of linear irreversible
thermodynamics beyond the near-equilibrium regime. In particular, the value
function is a thermodynamic potential that extends the classical dissipation
function and supplies the nonlinear relation between thermodynamics forces and
fluxes
Conformal Dimensions of Two-Derivative BMN Operators
We compute the anomalous dimensions of BMN operators with two covariant
derivative impurities at the planar level up to first order in the effective
coupling lambda'. The result equals those for two scalar impurities as well as
for mixed scalar and vector impurities given in the literature. Though the
results are the same, the computation is very different from the scalar case.
This is basically due to the existence of a non-vanishing overlap between the
derivative impurity and the ``background'' field Z. We present details of these
differences and their consequences.Comment: 27 pages, v2: references added, minor change
Ownership of co-creation assets: driving B2B value propositions in the service economy
The benefits of specialization have been driving the rise of the service economy and pushing capability frontiers and economic growth. In service economies, almost any activity, asset, and skill can be bought on competitive markets, making it harder to build competitive advantage on any of those inputs. Against that background, the question emerges what constitutes sustainable value propositions of service providers. Drawing on an emerging stream of research on the non-ownership value of services, we argue that service providers create value by taking on ownership of service assets and thereby transform uncertainty of value creation into economic opportunities. In our view, service providers offer the essential value proposition of transforming their clients’ uncertainty downsides into opportunities related to assets such as vehicles, real estate, equipment and computing platforms. Clients benefit by delegating ownership of assets to the domain of a service provider. In turn, clients can focus their investment on their most promising assets. Service providers create sustainable competitive advantage by assuming ownership and excelling at the management of (a) unique physical assets, (b) unique intangible assets and (c) maintaining an appropriate architecture of social capital through customer relationships and business ecosystems
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