127 research outputs found
Geometry of Higher-Dimensional Black Hole Thermodynamics
We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstr\"om
(RN) black holes in spacetime dimensions higher than four. These black holes
possess thermodynamic geometries similar to those in four dimensional
spacetime. The thermodynamic geometries are the Ruppeiner geometry and the
conformally related Weinhold geometry. The Ruppeiner geometry for Kerr
black hole is curved and divergent in the extremal limit. For Kerr
black hole there is no extremality but the Ruppeiner curvature diverges where
one suspects that the black hole becomes unstable. The Weinhold geometry of the
Kerr black hole in arbitrary dimension is a flat geometry. For RN black hole
the Ruppeiner geometry is flat in all spacetime dimensions, whereas its
Weinhold geometry is curved. In the Kerr black hole can possess more
than one angular momentum. Finally we discuss the Ruppeiner geometry for the
Kerr black hole in with double angular momenta.Comment: 8 pages, 2 figures, RevTex, References adde
All conformally flat pure radiation metrics
The complete class of conformally flat, pure radiation metrics is given,
generalising the metric recently given by Wils.Comment: 7 pages, plain Te
Riemann-Cartan Space-times of G\"odel Type
A class of Riemann-Cartan G\"odel-type space-times are examined in the light
of the equivalence problem techniques. The conditions for local space-time
homogeneity are derived, generalizing previous works on Riemannian G\"odel-type
space-times. The equivalence of Riemann-Cartan G\"odel-type space-times of this
class is studied. It is shown that they admit a five-dimensional group of
affine-isometries and are characterized by three essential parameters : identical triads () correspond to locally
equivalent manifolds. The algebraic types of the irreducible parts of the
curvature and torsion tensors are also presented.Comment: 24 pages, LaTeX fil
Whole grain foods and health - A Scandinavian perspective
The food-based dietary guidelines in the Scandinavian countries that recommend an intake of minimum 75 g whole grain per 10 MJ (2,388 kcal) per day are mainly derived from prospective cohort studies where quantitative but little qualitative details are available on whole grain products. The objective of the current paper is to clarify possible differences in nutritional and health effects of the types of whole grain grown and consumed in the Scandinavian countries. A further objective is to substantiate how processing may influence the nutritional value and potential health effects of different whole grains and whole grain foods. The most commonly consumed whole grain cereals in the Scandinavian countries are wheat, rye, and oats with a considerable inter-country variation in the consumption patterns and with barley constituting only a minor role. The chemical composition of these different whole grains and thus the whole grain products consumed vary considerably with regard to the content of macro- and micronutrients and bioactive components. A considerable amount of scientific substantiation shows that processing methods of the whole grains are important for the physiological and health effects of the final whole grain products. Future research should consider the specific properties of each cereal and its processing methods to further identify the uniqueness and health potentials of whole grain products. This would enable the authorities to provide more specific food-based dietary guidelines in relation to whole grain to the benefit of both the food industry and the consumer
The type N Karlhede bound is sharp
We present a family of four-dimensional Lorentzian manifolds whose invariant
classification requires the seventh covariant derivative of the curvature
tensor. The spacetimes in questions are null radiation, type N solutions on an
anti-de Sitter background. The large order of the bound is due to the fact that
these spacetimes are properly , i.e., curvature homogeneous of order 2
but non-homogeneous. This means that tetrad components of are constant, and that essential coordinates first appear as
components of . Covariant derivatives of orders 4,5,6 yield one
additional invariant each, and is needed for invariant
classification. Thus, our class proves that the bound of 7 on the order of the
covariant derivative, first established by Karlhede, is sharp. Our finding
corrects an outstanding assertion that invariant classification of
four-dimensional Lorentzian manifolds requires at most .Comment: 7 pages, typos corrected, added citation and acknowledgemen
Where are the trapped surfaces?
We discuss the boundary of the spacetime region through each point of which a
trapped surface passes, first in some simple soluble examples, and then in the
self-similar Vaidya solution. For the latter the boundary must lie strictly
inside the event horizon. We present a class of closed trapped surfaces
extending strictly outside the apparent horizon.Comment: 6 pages, 1 figure; talk at the Spanish Relativity Meeting ERE09 in
Bilba
On limits of spacetimes -- a coordinate-free approach
A coordinate-free approach to limits of spacetimes is developed. The limits
of the Schwarzschild metric as the mass parameter tends to 0 or are
studied, extending previous results. Besides the known Petrov type D and 0
limits, three vacuum plane-wave solutions of Petrov type N are found to be
limits of the Schwarzschild spacetime.Comment: 19 p
On the Symmetries of the Edgar-Ludwig Metric
The conformal Killing equations for the most general (non-plane wave)
conformally flat pure radiation field are solved to find the conformal Killing
vectors. As expected fifteen independent conformal Killing vectors exist, but
in general the metric admits no Killing or homothetic vectors. However for
certain special cases a one-dimensional group of homotheties or motions may
exist and in one very special case, overlooked by previous investigators, a
two-dimensional homethety group exists. No higher dimensional groups of motions
or homotheties are admitted by these metrics.Comment: Plain TeX, 7 pages, No figure
Equivalence of three-dimensional spacetimes
A solution to the equivalence problem in three-dimensional gravity is given
and a practically useful method to obtain a coordinate invariant description of
local geometry is presented. The method is a nontrivial adaptation of Karlhede
invariant classification of spacetimes of general relativity. The local
geometry is completely determined by the curvature tensor and a finite number
of its covariant derivatives in a frame where the components of the metric are
constants. The results are presented in the framework of real two-component
spinors in three-dimensional spacetimes, where the algebraic classifications of
the Ricci and Cotton-York spinors are given and their isotropy groups and
canonical forms are determined. As an application we discuss Goedel-type
spacetimes in three-dimensional General Relativity. The conditions for local
space and time homogeneity are derived and the equivalence of three-dimensional
Goedel-type spacetimes is studied and the results are compared with previous
works on four-dimensional Goedel-type spacetimes.Comment: 13 pages - content changes and corrected typo
Geometro-thermodynamics of tidal charged black holes
Tidal charged spherically symmetric vacuum brane black holes are
characterized by their mass m and tidal charge q, an imprint of the
5-dimensional Weyl curvature. For q>0 they are formally identical to the
Reissner-Nordstr\"om black hole of general relativity. We study the
thermodynamics and thermodynamic geometries of tidal charged black holes and
discuss similarities and differences as compared to the Reissner-Nordstr\"om
black hole. As a similarity, we show that (for q>0) the heat capacity of the
tidal charged black hole diverges on a set of measure zero of the parameter
space, nevertheless both the regularity of the Ruppeiner metric and a
Poincar\'e stability analysis shows no phase transition at those points. The
thermodynamic state spaces being different indicates that the underlying
statistical models could be different. We find that the q<0 parameter range,
which enhances the localization of gravity on the brane, is thermodynamically
preferred. Finally we constrain for the first time the possible range of the
tidal charge from the thermodynamic limit on gravitational radiation efficiency
at black hole mergers.Comment: v3: 23 pages, 8 figures, 1 table, published versio
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