共查询到20条相似文献,搜索用时 46 毫秒
1.
A general class of Lorentzian metrics,
,
, with
any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of H(x,u) with x at infinity determines many properties of geodesics. Essentially, a subquadratic growth of H ensures geodesic completeness and connectedness, while the critical situation appears when H(x,u) behaves in some direction as
, as in the classical model of exact gravitational waves. 相似文献
2.
Juri Agresti Roberto De Pietri Luca Lusanna Luca Martucci 《General Relativity and Gravitation》2004,36(5):1055-1134
In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy
, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO)
. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without
introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in
. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's
, which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation. 相似文献
3.
Stefano De Leo Zbigniew Oziewicz Waldyr A. Rodrigues Jayme Vaz 《International Journal of Theoretical Physics》1999,38(9):2349-2369
We formulate the variational principle of theDirac equation within the noncommutative even space-timesubalgebra, the Clifford
-algebra
. A fundamental ingredient in ourmultivectorial algebraic formulation is a
-complex geometry,
. We derive the Lagrangian for theDirac-Hestenes equation and show that it must be mapped on
, where denotes an
-algebra of functions. 相似文献
4.
On the Ricci Curvature of Compact Spacelike Hypersurfaces in Einstein Conformally Stationary-Closed Spacetimes 总被引:1,自引:0,他引:1
In this paper we develop an integral formula involving the Ricci and scalar curvatures of a compact spacelike hypersurface M in a spacetime
equipped with a timelike closed conformal vector field K (in short, conformally stationary-closed spacetime), and we apply it, when
is Einstein, in order to establish sufficient conditions for M to be a leaf of the foliation determined by K and to obtain some non-existence results. We also get some interesting consequences for the particular case when
is a generalized Robertson-Walker spacetime. 相似文献
5.
The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy
(where
0$$
" align="middle" border="0">
and
0$$
" align="middle" border="0">
are two constants). In particular, the perpendicular incidence of an electron with a given value
of the wave vector
is considered. The electron is forward-scattered into the region behind the barrier (region 2:
0$$
" align="middle" border="0">
), i. e. the wave function
is composed of plane waves with all wave vectors
such that
and
\left. 0 \right)} $$
" align="middle" border="0">
) (where
). Therefore, if
0$$
" align="middle" border="0">
, the wave function of the electron is represented as
, where
. An approximate formula is derived for the amplitude
. The authors pay a special attention to the flow density
and calculate this function in two cases: 1. for the plane
and 2. for high values of
is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier. 相似文献
6.
7.
Marcus Pivato 《Journal of statistical physics》2003,110(1-2):247-267
If
, and
is a finite (nonabelian) group, then
is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation
which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of
. We characterize when MCA are group endomorphisms of
, and show that MCA on
inherit a natural structure theory from the structure of
. We apply this structure theory to compute the measurable entropy of MCA, and to study convergence of initial measures to Haar measure. 相似文献
8.
We consider the Dirichlet Laplacian for astrip in
with one straight boundary and a width
, where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase,
, the operator has nobound statesfor small
.On the otherhand, a weakly bound state existsprovided
. In thatcase, there are positive c
1,c
2 suchthat the corresponding eigenvalue satisfies
for all
sufficiently small. 相似文献
9.
Varsha Daftardar-Gejji 《General Relativity and Gravitation》1998,30(5):695-700
Brinkmann has shown that conformally related Einstein spaces are either Ricci flat pp-waves or conformally flat spaces with one as de Sitter space and the other being flat. We herewith show that if gikand
are distinct metrics for which
, then both represent (generalised) pp-waves; and w,iis a homothetic conformal Killing vector of gik. It is further observed that in the situation
we can have many (and also non-conformally flat) conformally related solutions, unlike in Einstein spaces. In particular for perfect fluid coupling, we show that the conformally related solutions have to be Friedman-Robertson-Walker metrics with equation of state as
, or pp-waves depending on whether w,iis timelike, spacelike or null. 相似文献
10.
Let
be the Haag--Kastler net generated by the
(2) chiral current algebra at level 1. We classify the SL(2,
)-covariant subsystems
by showing that they are all fixed points nets
H
for some subgroup H of the gauge automorphisms group SO(3) of
. Then, using the fact that the net
1 generated by the
(1) chiral current can be regarded as a subsystem of
, we classify the subsystems of
1. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem
. 相似文献
11.
The product of two real spectral triples
and
, the first of which is necessarily even, was defined by A.Connes as
given by
and, in the even-even case, by
. Generically it is assumed that the real structure
obeys the relations
,
,
, where the
-sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes'
>-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this
-sign table. In this Letter, we propose an alternative definition of the product real structure such that the
-sign table is also satisfied by the product. 相似文献
12.
Ding-Xiong Wang 《General Relativity and Gravitation》1998,30(7):1025-1035
The effects of the Blandford-Znajek (BZ) process on the evolution of the central black holes of accretion disks are investigated. It is proved that the dimensionless angular momentum a* of the central black hole will evolve to a stable value
in the case of thin disks, while it will evolve to a stable value
in the case of thick disks. These results imply that the central black holes of accretion disks will never evolve to extreme Kerr black holes. 相似文献
13.
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group
in the following manner. There is a partition
into disjoint subsets and a bijection between
and the sectors
of the (p,q)-minimal model such that the fusion rules
correspond to
where
. 相似文献
14.
Given a simple, simply laced, complex Lie algebra
corresponding to the Lie group G, let
be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra
whose underlying graded commutative algebra is given by the cohomology, with respect to
, of the algebra of regular functions on G with values in
. We conjecture that
describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical
string. The conjecture is verified in the two explicitly known cases,
2 (the Virasoro string) and
3 (the
string). 相似文献
15.
Hans -Jürgen Seifert 《General Relativity and Gravitation》1971,1(3):247-259
A definition of a causal boundary
is given by assigning a future and a past endpoint to any non-extensible timelike or null line. A topology and a partial ordering can be introduced on
. The usual conditions for the causal structure can be formulated as properties of
. This boundary is compared with other types of boundaries.Read on 15 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General RelativityWork supported by the Deutsche Forschungsgemeinschaft. 相似文献
16.
We prove a simple formula for the transverse Poisson structure to a coadjoint orbit (in the dual of a Lie algebra
) and use it in examples such as
and
. We also give a sufficient condition on the isotropy subalgebra of
so that the transverse Poisson structureto the coadjoint orbit of is linear. 相似文献
17.
We show that there are canonical isomorphisms between Hochschild cohomology spaces
, where
is the algebra of smooth functions on a manifold M and
the space of skew multivector fields over M. This implies that continuous and differential deformation theories of
coincide. 相似文献
18.
We consider a class of fourth order theories of gravity with arbitrary matter fields arising from a diffeomorphism invariant Lagrangian density
, with
and
the phenomenological representation of the nongravitational fields. We derive first the generalization of the Einstein pseudotensor and the von Freud superpotential. We then show, using the arbitrariness that is always present in the choice of pseudotensor and superpotential, that we can choose these superpotentials to have the same form as those for the Hilbert Lagrangian of general relativity (GR). In particular we may introduce the Moller superpotential of GR as associated with a double-index differential conservation law. Similarly, using the Moller superpotential we prove that we can choose the Komar vector of GR to construct a conserved quantity for isolated asymptotically flat systems. For the example R + R2theory we prove then, that the active mass is equal to the total energy (or inertial mass) of the system. 相似文献
19.
A. Werthmüller A. Adamczak R. Jacot‐Guillarmod F. Mulhauser L.A. Schaller L. Schellenberg H. Schneuwly Y.‐A. Thalmann S. Tresch 《Hyperfine Interactions》1998,116(1-4):1-16
The charge exchange reaction of negative muons from the
atom to oxygen has been measured in gaseous mixtures of H2 + O2. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of
, describing the transfer from the ground state of thermalized
atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the
thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate
=3.9
1011 s-1 in the energy interval 0.12–0.22 eV. The analysis with the model of Two components shows that all measured time spectra can be reproduced with the same set of parameters. 相似文献
20.
The universal R-matrix for a class of esoteric (nonstandard) quantum groups
q(gl(2N+1)) is constructed as a twisting of the universal R-matrix
S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle
is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's
(N)
q (gl(2N+1))), providing the factorization property of
. As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo. 相似文献