146 research outputs found
CYK Tensors, Maxwell Field and Conserved Quantities for Spin-2 Field
Starting from an important application of Conformal Yano--Killing tensors for
the existence of global charges in gravity, some new observations at \scri^+
are given. They allow to define asymptotic charges (at future null infinity) in
terms of the Weyl tensor together with their fluxes through \scri^+. It
occurs that some of them play a role of obstructions for the existence of
angular momentum.
Moreover, new relations between solutions of the Maxwell equations and the
spin-2 field are given. They are used in the construction of new conserved
quantities which are quadratic in terms of the Weyl tensor. The obtained
formulae are similar to the functionals obtained from the
Bel--Robinson tensor.Comment: 20 pages, LaTe
Rigid spheres in Riemannian spaces
Choice of an appropriate (3+1)-foliation of spacetime or a (2+1)-foliation of
the Cauchy space, leads often to a substantial simplification of various
mathematical problems in General Relativity Theory. We propose a new method to
construct such foliations. For this purpose we define a special family of
topological two-spheres, which we call "rigid spheres". We prove that there is
a four-parameter family of rigid spheres in a generic Riemannian three-manifold
(in case of the flat Euclidean three-space these four parameters are: 3
coordinates of the center and the radius of the sphere). The rigid spheres can
be used as building blocks for various ("spherical", "bispherical" etc.)
foliations of the Cauchy space. This way a supertranslation ambiguity may be
avoided. Generalization to the full 4D case is discussed. Our results
generalize both the Huang foliations (cf. \cite{LHH}) and the foliations used
by us (cf. \cite{JKL}) in the analysis of the two-body problem.Comment: 23 page
Energy and angular momentum of the weak gravitational waves on the Schwarzschild background -- quasilocal gauge-invariant formulation
It is shown that the axial and polar perturbations of the spherically
symmetric black hole can be described in a gauge-invariant way. The reduced
phase space describing gravitational waves outside of the horizon is described
by the gauge-invariant quantities. Both degrees of freedom fulfill generalized
scalar wave equation. For the axial degree of freedom the radial part of the
equation corresponds to the Regge-Wheeler result (Phys. Rev. 108, 1063-1069
(1957)) and for the polar one we get Zerilli result (Phys. Rev. D2, 2141-2160
(1970)), see also Chandrasekhar (The Mathematical Theory of Black
Holes,(Clarendon Press Oxford, 1983)), Moncrief (Annals of Physics 88, 323-342
(1974)) for both. An important ingredient of the analysis is the concept of
quasilocality which does duty for the separation of the angular variables in
the usual approach. Moreover, there is no need to represent perturbations by
normal modes (with time dependence ), we have fields in spacetime
and the Cauchy problem for them is well defined outside of the horizon. The
reduced symplectic structure explains the origin of the axial and polar
invariants. It allows to introduce an energy and angular momentum for the
gravitational waves which is invariant with respect to the gauge
transformations. Both generators represent quadratic approximation of the ADM
nonlinear formulae in terms of the perturbations of the Schwarzschild metric.
We also discuss the boundary-initial value problem for the linearized Einstein
equations on a Schwarzschild background outside of the horizon.Comment: 23 page
Asymptotic Conformal Yano--Killing Tensors for Schwarzschild Metric
The asymptotic conformal Yano--Killing tensor proposed in J. Jezierski, On
the relation between metric and spin-2 formulation of linearized Einstein
theory [GRG, in print (1994)] is analyzed for Schwarzschild metric and tensor
equations defining this object are given. The result shows that the
Schwarzschild metric (and other metrics which are asymptotically
``Schwarzschildean'' up to O(1/r^2) at spatial infinity) is among the metrics
fullfilling stronger asymptotic conditions and supertranslations ambiguities
disappear. It is also clear from the result that 14 asymptotic gravitational
charges are well defined on the ``Schwarzschildean'' background.Comment: 8 pages, latex, no figure
Dynamics of a self gravitating light-like matter shell: a gauge-invariant Lagrangian and Hamiltonian description
A complete Lagrangian and Hamiltonian description of the theory of
self-gravitating light-like matter shells is given in terms of
gauge-independent geometric quantities. For this purpose the notion of an
extrinsic curvature for a null-like hypersurface is discussed and the
corresponding Gauss-Codazzi equations are proved. These equations imply Bianchi
identities for spacetimes with null-like, singular curvature. Energy-momentum
tensor-density of a light-like matter shell is unambiguously defined in terms
of an invariant matter Lagrangian density. Noether identity and
Belinfante-Rosenfeld theorem for such a tensor-density are proved. Finally, the
Hamiltonian dynamics of the interacting system: ``gravity + matter'' is derived
from the total Lagrangian, the latter being an invariant scalar density.Comment: 20 pages, RevTeX4, no figure
Semimetalic antiferromagnetism in the half-Heusler compound CuMnSb
The half-Heusler compound CuMnSb, the first antiferromagnet (AFM) in the
Mn-based class of Heuslers and half-Heuslers that contains several conventional
and half metallic ferromagnets, shows a peculiar stability of its magnetic
order in high magnetic fields. Density functional based studies reveal an
unusual nature of its unstable (and therefore unseen) paramagnetic state, which
for one electron less (CuMnSn, for example) would be a zero gap semiconductor
(accidentally so) between two sets of very narrow, topologically separate bands
of Mn 3d character. The extremely flat Mn 3d bands result from the environment:
Mn has four tetrahedrally coordinated Cu atoms whose 3d states lie well below
the Fermi level, and the other four tetrahedrally coordinated sites are empty,
leaving chemically isolated Mn 3d states. The AFM phase can be pictured
heuristically as a self-doped CuMnSb compensated semimetal
with heavy mass electrons and light mass holes, with magnetic coupling
proceeding through Kondo and/or antiKondo coupling separately through the two
carrier types. The ratio of the linear specific heat coefficient and the
calculated Fermi level density of states indicates a large mass enhancement
, or larger if a correlated band structure is taken as the
reference
Unexpected coexisting solid solutions in the quasi-binary Ag(II)F2/Cu(II)F2 phase diagram
High-temperature solid-state reaction between orthorhombic AgF2 and
monoclinic CuF2 (y = 0.15, 0.3, 0.4, 0.5) in a fluorine atmosphere resulted in
coexisting solid solutions of Cu-poor orthorhombic and Cu-rich monoclinic
phases with stoichiometry Ag1-xCuxF2. Based on X-ray powder diffraction
analyses, the mutual solubility in the orthorhombic phase (AgF2 doped with Cu)
appears to be at an upper limit of Cu concentration of 30 mol % (Ag0.7Cu0.3F2),
while the monoclinic phase (CuF2 doped with Ag) can form a nearly
stoichiometric Cu : Ag = 1 : 1 solid solution (Cu0.56Ag0.44F2), preserving the
CuF2 crystal structure. Experimental data and DFT calculations showed that AgF2
doped with Cu and CuF2 doped with Ag solid solutions deviate from the classical
Vegards law. Magnetic measurements of Ag1-xCuxF2 showed that the Neel
temperature (TN) decreases with increasing Cu content in both phases. Likewise,
theoretical DFT+U calculations for Ag1-xCuxF2 showed that the progressive
substitution of Ag by Cu decreases the magnetic interaction strength (J2D) in
both structures. Electrical conductivity measurements of Ag0.85Cu0.15F2 showed
a ca. 2-fold increase in specific ionic conductivity (3.71 x 10-13 plus/minus
2.6 x 10-15 S/cm) as compared to pure AgF2 (1.85 x 10-13 plus/minus 1.2 x 10-15
S/cm), indicating the formation of a vacancy- or F adatom-free metal difluoride
sample.Comment: 9 pages, 4 figures, 1 Table, and electronic supplement of 14 page
Trapped surfaces and the Penrose inequality in spherically symmetric geometries
We demonstrate that the Penrose inequality is valid for spherically symmetric
geometries even when the horizon is immersed in matter. The matter field need
not be at rest. The only restriction is that the source satisfies the weak
energy condition outside the horizon. No restrictions are placed on the matter
inside the horizon. The proof of the Penrose inequality gives a new necessary
condition for the formation of trapped surfaces. This formulation can also be
adapted to give a sufficient condition. We show that a modification of the
Penrose inequality proposed by Gibbons for charged black holes can be broken in
early stages of gravitational collapse. This investigation is based exclusively
on the initial data formulation of General Relativity.Comment: plain te
Conserved superenergy currents
We exploit once again the analogy between the energy-momentum tensor and the
so-called ``superenergy'' tensors in order to build conserved currents in the
presence of Killing vectors. First of all, we derive the divergence-free
property of the gravitational superenergy currents under very general
circumstances, even if the superenergy tensor is not divergence-free itself.
The associated conserved quantities are explicitly computed for the
Reissner-Nordstrom and Schwarzschild solutions. The remaining cases, when the
above currents are not conserved, lead to the possibility of an interchange of
some superenergy quantities between the gravitational and other physical fields
in such a manner that the total, mixed, current may be conserved. Actually,
this possibility has been recently proved to hold for the Einstein-Klein-Gordon
system of field equations. By using an adequate family of known exact
solutions, we present explicit and completely non-obvious examples of such
mixed conserved currents.Comment: LaTeX, 19 pages; improved version adding new content to the second
section and some minor correction
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