2,615 research outputs found
Variational Principles for Natural Divergence-free Tensors in Metric Field Theories
Let be a system of differential equations for the
components of a metric tensor on . Suppose that transforms
tensorially under the action of the diffeomorphism group on metrics and that
the covariant divergence of vanishes. We then prove that is
the Euler-Lagrange expression some Lagrangian density provided that is
of third order. Our result extends the classical works of Cartan, Weyl,
Vermeil, Lovelock, and Takens on identifying field equations for the metric
tensor with the symmetries and conservation laws of the Einstein equations
On the static Lovelock black holes
We consider static spherically symmetric Lovelock black holes and generalize
the dimensionally continued black holes in such a way that they asymptotically
for large r go over to the d-dimensional Schwarzschild black hole in dS/AdS
spacetime. This means that the master algebraic polynomial is not degenerate
but instead its derivative is degenerate. This family of solutions contains an
interesting class of pure Lovelock black holes which are the Nth order Lovelock
{\Lambda}-vacuum solu- tions having the remarkable property that their
thermodynamical parameters have the universal character in terms of the event
horizon radius. This is in fact a characterizing property of pure Lovelock
theories. We also demonstrate the universality of the asymptotic Einstein limit
for the Lovelock black holes in general.Comment: 19 page
Daisyworld: a review
Daisyworld is a simple planetary model designed to show the long-term effects of coupling between life and its environment. Its original form was introduced by James Lovelock as a defense against criticism that his Gaia theory of the Earth as a self-regulating homeostatic system requires teleological control rather than being an emergent property. The central premise, that living organisms can have major effects on the climate system, is no longer controversial. The Daisyworld model has attracted considerable interest from the scientific community and has now established itself as a model independent of, but still related to, the Gaia theory. Used widely as both a teaching tool and as a basis for more complex studies of feedback systems, it has also become an important paradigm for the understanding of the role of biotic components when modeling the Earth system. This paper collects the accumulated knowledge from the study of Daisyworld and provides the reader with a concise account of its important properties. We emphasize the increasing amount of exact analytic work on Daisyworld and are able to bring together and summarize these results from different systems for the first time. We conclude by suggesting what a more general model of life-environment interaction should be based on
Quantized Friction across Ionic Liquid Thin Films
Ionic liquids, salts in the liquid state under ambient conditions, are of
great interest as precision lubricants. Ionic liquids form layered structures
at surfaces, yet it is not clear how this nano-structure relates to their
lubrication properties. We measured the friction force between atomically
smooth solid surfaces across ionic liquid films of controlled thickness in
terms of the number of ion layers. Multiple friction-load regimes emerge, each
corresponding to a different number of ion layers in the film. In contrast to
molecular liquids, the friction coefficients differ for each layer due to their
varying composition
Positioning the Destination Product-Can Regional Tourist Boards Learn from Private Sector Practice?
This article examines the role of positioning in the
marketing of a tourism destination. The study focuses on the current positioning strategies pursued by the Regional Tourist Boards (RTBs) in England. A recent nationwide consumer research study into short holiday destination choice in the UK revealed that consumers were confused by the regional product message. The evidence suggests that current RTB positioning strategies are failing to keep pace with the constantly evolving needs of the consumer. This
article explores the reasons for clearly positioning the destination product and suggests that, although RTBs could learn from marketing strategies employed in other sectors of the tourism industry, there are likely to be organisational and cultural barriers inhibiting this
learning curve
Conserved Matter Superenergy Currents for Hypersurface Orthogonal Killing Vectors
We show that for hypersurface orthogonal Killing vectors, the corresponding
Chevreton superenergy currents will be conserved and proportional to the
Killing vectors. This holds for four-dimensional Einstein-Maxwell spacetimes
with an electromagnetic field that is sourcefree and inherits the symmetry of
the spacetime. A similar result also holds for the trace of the Chevreton
tensor. The corresponding Bel currents have previously been proven to be
conserved and our result can be seen as giving further support to the concept
of conserved mixed superenergy currents. The analogous case for a scalar field
has also previously been proven to give conserved currents and we show, for
completeness, that these currents also are proportional to the Killing vectors.Comment: 13 page
Algebraic Rainich theory and antisymmetrisation in higher dimensions
The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient
conditions on an energy-momentum tensor to be that of a Maxwell field (a
2-form) in four dimensions. Via Einstein's equations these conditions can be
expressed in terms of the Ricci tensor, thus providing conditions on a
spacetime geometry for it to be an Einstein-Maxwell spacetime. One of the
conditions is that is proportional to the metric, and it has previously
been shown in arbitrary dimension that any tensor satisfying this condition is
a superenergy tensor of a simple -form. Here we examine algebraic Rainich
conditions for general -forms in higher dimensions and their relations to
identities by antisymmetrisation. Using antisymmetrisation techniques we find
new identities for superenergy tensors of these general (non-simple) forms, and
we also prove in some cases the converse; that the identities are sufficient to
determine the form. As an example we obtain the complete generalisation of the
classical Rainich theory to five dimensions.Comment: 16 pages, LaTe
The Lanczos potential for Weyl-candidate tensors exists only in four dimensions
We prove that a Lanczos potential L_abc for the Weyl candidate tensor W_abcd
does not generally exist for dimensions higher than four. The technique is
simply to assume the existence of such a potential in dimension n, and then
check the integrability conditions for the assumed system of differential
equations; if the integrability conditions yield another non-trivial
differential system for L_abc and W_abcd, then this system's integrability
conditions should be checked; and so on. When we find a non-trivial condition
involving only W_abcd and its derivatives, then clearly Weyl candidate tensors
failing to satisfy that condition cannot be written in terms of a Lanczos
potential L_abc.Comment: 11 pages, LaTeX, Heavily revised April 200
Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups
In a previous paper we showed that the electromagnetic superenergy tensor,
the Chevreton tensor, gives rise to a conserved current when there is a
hypersurface orthogonal Killing vector present. In addition, the current is
proportional to the Killing vector. The aim of this paper is to extend this
result to the case when we have a two-parameter Abelian isometry group that
acts orthogonally transitive on non-null surfaces. It is shown that for
four-dimensional Einstein-Maxwell theory with a source-free electromagnetic
field, the corresponding superenergy currents lie in the orbits of the group
and are conserved. A similar result is also shown to hold for the trace of the
Chevreton tensor and for the Bach tensor, and also in Einstein-Klein-Gordon
theory for the superenergy of the scalar field. This links up well with the
fact that the Bel tensor has these properties and the possibility of
constructing conserved mixed currents between the gravitational field and the
matter fields.Comment: 15 page
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