65 research outputs found
Trajectories in a space with a spherically symmetric dislocation
We consider a new type of defect in the scope of linear elasticity theory,
using geometrical methods. This defect is produced by a spherically symmetric
dislocation, or ball dislocation. We derive the induced metric as well as the
affine connections and curvature tensors. Since the induced metric is
discontinuous, one can expect ambiguity coming from these quantities, due to
products between delta functions or its derivatives, plaguing a description of
ball dislocations based on the Geometric Theory of Defects. However, exactly as
in the previous case of cylindric defect, one can obtain some well-defined
physical predictions of the induced geometry. In particular, we explore some
properties of test particle trajectories around the defect and show that these
trajectories are curved but can not be circular orbits.Comment: 11 pages, 3 figure
Absolute conservation law for black holes
In all 2d theories of gravity a conservation law connects the (space-time
dependent) mass aspect function at all times and all radii with an integral of
the matter fields. It depends on an arbitrary constant which may be interpreted
as determining the initial value together with the initial values for the
matter field. We discuss this for spherically reduced Einstein-gravity in a
diagonal metric and in a Bondi-Sachs metric using the first order formulation
of spherically reduced gravity, which allows easy and direct fixations of any
type of gauge. The relation of our conserved quantity to the ADM and Bondi mass
is investigated. Further possible applications (ideal fluid, black holes in
higher dimensions or AdS spacetimes etc.) are straightforward generalizations.Comment: LaTex, 17 pages, final version, to appear in Phys. Rev.
Universal conservation law and modified Noether symmetry in 2d models of gravity with matter
It is well-known that all 2d models of gravity---including theories with
nonvanishing torsion and dilaton theories---can be solved exactly, if matter
interactions are absent. An absolutely (in space and time) conserved quantity
determines the global classification of all (classical) solutions. For the
special case of spherically reduced Einstein gravity it coincides with the mass
in the Schwarzschild solution. The corresponding Noether symmetry has been
derived previously by P. Widerin and one of the authors (W.K.) for a specific
2d model with nonvanishing torsion. In the present paper this is generalized to
all covariant 2d theories, including interactions with matter. The related
Noether-like symmetry differs from the usual one. The parameters for the
symmetry transformation of the geometric part and those of the matterfields are
distinct. The total conservation law (a zero-form current) results from a two
stage argument which also involves a consistency condition expressed by the
conservation of a one-form matter ``current''. The black hole is treated as a
special case.Comment: 3
Geometric Interpretation and Classification of Global Solutions in Generalized Dilaton Gravity
Two dimensional gravity with torsion is proved to be equivalent to special
types of generalized 2d dilaton gravity. E.g. in one version, the dilaton field
is shown to be expressible by the extra scalar curvature, constructed for an
independent Lorentz connection corresponding to a nontrivial torsion.
Elimination of that dilaton field yields an equivalent torsionless theory,
nonpolynomial in curvature. These theories, although locally equivalent exhibit
quite different global properties of the general solution. We discuss the
example of a (torsionless) dilaton theory equivalent to the --model.
Each global solution of this model is shown to split into a set of global
solutions of generalized dilaton gravity. In contrast to the theory with
torsion the equivalent dilaton one exhibits solutions which are asymptotically
flat in special ranges of the parameters. In the simplest case of ordinary
dilaton gravity we clarify the well known problem of removing the Schwarzschild
singularity by a field redefinition.Comment: 21 pages, 6 Postscript figure
The Universality of Einstein Equations
It is shown that for a wide class of analytic Lagrangians which depend only
on the scalar curvature of a metric and a connection, the application of the
so--called ``Palatini formalism'', i.e., treating the metric and the connection
as independent variables, leads to ``universal'' equations. If the dimension
of space--time is greater than two these universal equations are Einstein
equations for a generic Lagrangian and are suitably replaced by other universal
equations at bifurcation points. We show that bifurcations take place in
particular for conformally invariant Lagrangians and prove
that their solutions are conformally equivalent to solutions of Einstein
equations. For 2--dimensional space--time we find instead that the universal
equation is always the equation of constant scalar curvature; the connection in
this case is a Weyl connection, containing the Levi--Civita connection of the
metric and an additional vectorfield ensuing from conformal invariance. As an
example, we investigate in detail some polynomial Lagrangians and discuss their
bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9
Renal Fanconi Syndrome and Hypophosphatemic Rickets in the Absence of Xenotropic and Polytropic Retroviral Receptor in the Nephron.
Tight control of extracellular and intracellular inorganic phosphate (Pi) levels is critical to most biochemical and physiologic processes. Urinary Pi is freely filtered at the kidney glomerulus and is reabsorbed in the renal tubule by the action of the apical sodium-dependent phosphate transporters, NaPi-IIa/NaPi-IIc/Pit2. However, the molecular identity of the protein(s) participating in the basolateral Pi efflux remains unknown. Evidence has suggested that xenotropic and polytropic retroviral receptor 1 (XPR1) might be involved in this process. Here, we show that conditional inactivation of Xpr1 in the renal tubule in mice resulted in impaired renal Pi reabsorption. Analysis of Pi transport in primary cultures of proximal tubular cells or in freshly isolated renal tubules revealed that this Xpr1 deficiency significantly affected Pi efflux. Further, mice with conditional inactivation of Xpr1 in the renal tubule exhibited generalized proximal tubular dysfunction indicative of Fanconi syndrome, characterized by glycosuria, aminoaciduria, calciuria, and albuminuria. Dramatic alterations in the renal transcriptome, including a significant reduction in NaPi-IIa/NaPi-IIc expression, accompanied these functional changes. Additionally, Xpr1-deficient mice developed hypophosphatemic rickets secondary to renal dysfunction. These results identify XPR1 as a major regulator of Pi homeostasis and as a potential therapeutic target in bone and kidney disorders
Towards complete integrability of two dimensional Poincar\'e gauge gravity
It is shown that gravity on the line can be described by the two dimensional
(2D) Hilbert-Einstein Lagrangian supplemented by a kinetic term for the coframe
and a translational {\it boundary} term. The resulting model is equivalent to a
Yang-Mills theory of local {\it translations} and frozen Lorentz gauge degrees.
We will show that this restricted Poincar\'e gauge model in 2 dimensions is
completely integrable. {\it Exact} wave, charged black hole, and `dilaton'
solutions are then readily found. In vacuum, the integrability of the {\it
general} 2D Poincar\'e gauge theory is formally proved along the same line of
reasoning.Comment: 35 pages, report Cologne-thp-1993-H
Positive specific heat of the quantum corrected dilaton black hole
Path integral quantization of dilaton gravity in two dimensions is applied to
the CGHS model to the first nontrivial order in matter loops. Our approach is
background independent as geometry is integrated out exactly. The result is an
effective shift of the Killing norm: the apparent horizon becomes smaller. The
Hawking temperature which is constant to leading order receives a quantum
correction. As a consequence, the specific heat becomes positive and
proportional to the square of the black hole mass.Comment: 18 pages, JHEP style, 1 eps figure, v2: extended the discussion,
added new formulas for mass change, added three new references (in particular
[35]
Classical self-forces in a space with a dispiration
We derive the gravitational and electrostatic self-energies of a particle at
rest in the background of a cosmic dispiration (topological defect), finding
that the particle may experience potential steps, well potentials or potential
barriers depending on the nature of the interaction and also on certain
properties of the defect. The results may turn out to be useful in cosmology
and condensed matter physics.Comment: 5 pages, 4 figures, revtex4 fil
Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying Approach
We provide a concise approach to generalized dilaton theories with and
without torsion and coupling to Yang-Mills fields. Transformations on the space
of fields are used to trivialize the field equations locally. In this way their
solution becomes accessible within a few lines of calculation only. In this
first of a series of papers we set the stage for a thorough global
investigation of classical and quantum aspects of more or less all available 2D
gravity-Yang-Mills models.Comment: 24 pages, no figures, some sign errors in Eqs. 52--59 have been
corrected (according to the Erratum
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