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1.
Type O pure radiation metrics with a cosmological constant 总被引:1,自引:1,他引:0
In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant
Λ, and , by considering the case . This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes
where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction
(from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred
to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation
spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case
) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors. 相似文献
2.
H. Backe A. Dretzke R. Horn T. Kolb W. Lauth R. Repnow M. Sewtz N. Trautmann 《Hyperfine Interactions》2005,162(1-4):77-84
Drift time measurements of ions in a buffer gas cell filled with argon have been performed from which changes of the ion mobility
and ionic radii for various heavy elements and their compounds were determined. The ionic radius of americium shrinks by (3.1
1.3)% with respect to that of plutonium, and an increase of the radius by (28 2)% of plutonium oxide with respect to plutonium was found. Ion chemical reactions of erbium ions were studied online in
an argon buffer gas cell to which the reaction gases oxygen (O) and methane (CH) were added. The erbium ions were implanted into the buffer gas cell with an energy of 50 MeV. The online measured reaction
constant = (3.2 0.4) 10 cm/(molecule s) for the reaction Er + O
ErO + O agrees with a reference measurement = (3.6 0.4) 10 cm/(molecule s), performed with a Fourier-Transform-Mass-Spectrometer. 相似文献
3.
A new parametrization of the 3-metric allows to find explicitly a York map by means of a partial Shanmugadhasan canonical
transformation in canonical ADM tetrad gravity. This allows to identify the two pairs of physical tidal degrees of freedom
(the Dirac observables of the gravitational field have to be built in term of them) and 14 gauge variables. These gauge quantities,
whose role in describing generalized inertial effects is clarified, are all configurational except one, the York time, i.e.
the trace of the extrinsic curvature of the instantaneous 3-spaces (corresponding to a clock synchronization convention) of a non-inertial frame centered on an arbitrary observer. In the Dirac Hamiltonian is the sum of the weak ADM energy (whose density is coordinate-dependent, containing the inertial potentials) and of the first-class constraints. The main results of the
paper, deriving from a coherent use of constraint theory, are: (i) The explicit form of the Hamilton equations for the two
tidal degrees of freedom of the gravitational field in an arbitrary gauge: a deterministic evolution can be defined only in
a completely fixed gauge, i.e. in a non-inertial frame with its pattern of inertial forces. The simplest such gauge is the
3-orthogonal one, but other gauges are discussed and the Hamiltonian interpretation of the harmonic gauges is given. This
frame-dependence derives from the geometrical view of the gravitational field and is lost when the theory is reduced to a
linear spin 2 field on a background space-time. (ii) A general solution of the super-momentum constraints, which shows the
existence of a generalized Gribov ambiguity associated to the 3-diffeomorphism gauge group. It influences: (a) the explicit
form of the solution of the super-momentum constraint and then of the Dirac Hamiltonian; (b) the determination of the shift
functions and then of the lapse one. (iii) The dependence of the Hamilton equations for the two pairs of dynamical gravitational
degrees of freedom (the generalized tidal effects) and for the matter, written in a completely fixed 3-orthogonal Schwinger
time gauge, upon the gauge variable , determining the convention of clock synchronization. The associated relativistic inertial effects, absent in Newtonian
gravity and implying inertial forces changing from attractive to repulsive in regions with different sign of , are completely unexplored and may have astrophysical relevance in the interpretation of the dark side of the universe. 相似文献
4.
J. Ponce de Leon 《General Relativity and Gravitation》2006,38(1):61-81
Braneworld theory provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Non-static
extra dimensions can generally lead to a variable vacuum energy, which in turn may explain the present accelerated cosmic
expansion. We concentrate our attention in models where the vacuum energy decreases as an inverse power law of the scale factor.
These models agree with the observed accelerating universe, while fitting simultaneously the observational data for the density
and deceleration parameter. The redshift at which the vacuum energy can start to dominate depends on the mass density of ordinary
matter. For
m
= 0.3, the transition from decelerated to accelerated cosmic expansion occurs at z
T
≈ 0.48 ± 0.20, which is compatible with SNe data. We set a lower bound on the deceleration parameter today, namely > − 1 + 3
m
/2, i.e., > − 0.55 for
m
= 0.3. The future evolution of the universe crucially depends on the time when vacuum starts to dominate over ordinary matter.
If it dominates only recently, at an epoch z < 0.64, then the universe is accelerating today and will continue that way forever. If vacuum dominates earlier, at z > 0.64, then the deceleration comes back and the universe recollapses at some point in the distant future. In the first case,
quintessence and Cardassian expansion can be formally interpreted as the low energy limit of our model, although they are
entirely different in philosophy. In the second case there is no correspondence between these models and ours. 相似文献
5.
Tadayoshi Adachi 《Letters in Mathematical Physics》2007,82(1):1-8
For an N-body Stark Hamiltonian , the resolvent estimate holds uniformly in with Re and Im , where , and is a compact interval. This estimate is well known as the limiting absorption principle. In this paper, we report that by
introducing the localization in the configuration space, a refined resolvent estimate holds uniformly in with Re and Im .
Dedicated to Professor Hideo Tamura on the occasion of his 60th birthday 相似文献
6.
Maxim Samsonov 《Letters in Mathematical Physics》2006,75(1):63-77
A problem of defining the quantum analogues for semi-classical twists in U()[[t]] is considered. First, we study specialization at q = 1 of singular coboundary twists defined in Uq ())[[t]] for g being a nonexceptional Lie algebra, then we consider specialization of noncoboundary twists when = and obtain q-deformation of the semiclassical twist introduced by Connes and Moscovici in noncommutative geometry.
Mathematics Subject Classification: 16W30, 17B37, 81R50 相似文献
7.
C. F. C. Brandt R. Chan M. A. F. da Silva Jaime F. Villas da Rocha 《General Relativity and Gravitation》2007,39(10):1675-1687
We study the evolution of an inhomogeneous fluid with self-similarity of the second kind and anisotropic pressure. We found
a class of solution to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid
is proportional to its energy density () and that the fluid moves along time-like geodesics. The equation of state combined with the self-similarity of second kind
implies ω = −1. The energy conditions, geometrical and physical properties of the solutions are studied. We have found that,
for the self-similar parameter , the solution represents an accelerated cosmological model ending in a Big Rip stage. 相似文献
8.
A new model is proposed to a collapsing radiating star consisting of an isotropic fluid with shear viscosity undergoing radial
heat flow with outgoing radiation. In a previous paper we have introduced a function time dependent into the g
rr
, besides the time dependent metric functions and . The aim of this work is to generalize this previous model by introducing shear viscosity and compare it to the non-viscous
collapse. The behavior of the density, pressure, mass, luminosity and the effective adiabatic index is analyzed. Our work
is compared to the case of a collapsing shearing fluid of a previous model, for a star with 6 . The pressure of the star, at the beginning of the collapse, is isotropic but due to the presence of the shear the pressure
becomes more and more anisotropic. The black hole is never formed because the apparent horizon formation condition is never
satisfied. An observer at infinity sees a radial point source radiating exponentially until reaches the time of maximum luminosity
and suddenly the star turns off. The effective adiabatic index has a very unusual behavior because we have a non-adiabatic
regime in the fluid due to the heat flow. 相似文献
9.
O. W. Greenberg 《Foundations of Physics》2006,36(10):1535-1553
Lüders and Pauli proved the theorem based on Lagrangian quantum field theory almost half a century ago. Jost gave a more general proof based on “axiomatic” field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why is fundamental—because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the transform of any relativistic field without calculating , and separately and then multiplying them. The purpose of this pedagogical paper is to “deaxiomatize” the theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary. 相似文献
10.
We have quantized a flat cosmological model in the context of the metric models, using the causal Bohmian quantum theory. The equations are solved and then we have obtained how the quantum corrections
influence the classical equations. 相似文献
11.
Marek Biskup Lincoln Chayes Shannon Starr 《Communications in Mathematical Physics》2007,269(3):611-657
We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins satisfy . From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with . The most notable examples are the quantum orbital-compass model on and the quantum 120-degree model on which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. 相似文献
12.
We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W
n
(S), and rooted self-avoiding polygons P
n
(S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P
n
(S), and W
n(S) for an arbitrary point S on the lattice. These are used to compute the averages ,, and over different positions of S. We find that the connectivity constant μ, and the radius of gyration exponent are the same for the annealed and quenched averages. However, , and , where the exponents and , take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives and , to be compared with the known annealed values and . 相似文献
13.
In this paper we obtain a height estimate concerning compact space-like hypersurfaces Σ
n
immersed with some positive constant r-mean curvature into an (n + 1)-dimensional Lorentzian product space , and whose boundary is contained into a slice {t} × M
n
. By considering the hyperbolic caps of the Lorentz–Minkowski space , we show that our estimate is sharp. Furthermore, we apply this estimate to study the complete space-like hypersurfaces
immersed with some positive constant r-mean curvature into a Lorentzian product space. For instance, when the ambient space–time is spatially closed, we show that
such hypersurfaces must satisfy the topological property of having more than one end which constitutes a necessary condition
for their existence. 相似文献
14.
David Gérard-Varet 《Communications in Mathematical Physics》2009,286(1):81-110
We consider the Navier-Stokes equation in a domain with irregular boundaries. The irregularity is modeled by a spatially homogeneous
random process, with typical size . In the parent paper [8], we derived a homogenized boundary condition of Navier type as . We show here that for a large class of boundaries, this Navier condition provides a approximation in L
2, instead of for periodic irregularities. Our result relies on the study of an auxiliary boundary layer system. Decay properties of this
boundary layer are deduced from a central limit theorem for dependent variables. 相似文献
15.
Asao Arai 《Letters in Mathematical Physics》2006,77(3):283-290
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral
of a family of self-adjoint operators
acting in the Hilbert space
, where
is the Hilbert space of the quantum radiation field. The fiber operator
is called the Hamiltonian of the Dirac polaron with total momentum
. The main result of this paper is concerned with the non-relativistic (scaling) limit of
. It is proven that the non-relativistic limit of
yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics. 相似文献
16.
Domingos H. U. Marchetti 《Journal of statistical physics》1990,61(3-4):909-911
A simple argument is presented by which one can show that the critical inverse temperature
c
of a two-dimensional Coulomb gas (standard or hard-core) with activityz satisfies
, where
in the low-activity limit. Previous results yield
. 相似文献
17.
We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open set
with the Dirichlet boundary condition. This is done in terms of the interior capacitary radius of Ω which is defined as the
maximal possible radius of a ball B with a negligible intersection with the complement of Ω. Here negligibility of
means that cap(F)≤ γ cap (B), where cap a means the Wiener (harmonic) capacity and
is arbitrarily fixed with the sole restriction
. We provide explicit values of constants in the two-sided estimates. 相似文献
18.
For convex co-compact hyperbolic quotients , we analyze the long-time asymptotic of the solution of the wave equation u(t) with smooth compactly supported initial data f = (f
0, f
1). We show that, if the Hausdorff dimension δ of the limit set is less than n/2, then where and . We explain, in terms of conformal theory of the conformal infinity of X, the special cases , where the leading asymptotic term vanishes. In a second part, we show for all the existence of an infinite number of resonances (and thus zeros of Selberg zeta function) in the strip . As a byproduct we obtain a lower bound on the remainder R(t) for generic initial data f. 相似文献
19.
In modelling complex systems as real diffusion processes it is common to analyse its diffusive regime through the study of approximating sequences of random walks. For the partial sums one considers the approximating sequence of processes . Then, under sufficient smoothness requirements we have the convergence to the desired diffusion, . A key assumption usually presumed is the finiteness of the second moment, and, hence the validity of the Central Limit Theorem. Under anomalous diffusive regime the asymptotic behavior of S
n may well be non-Gaussian and . Such random walks have been referred by physicists as Lévy motions or Lévy flights. In this work, we introduce an alternative notion to classify these regimes, the diffusion index . For some properly chosen let . Relationship between , the infinitesimal diffusion coefficients and the diffusion constant will be explored. Illustrative examples as well as estimates, based on extreme order statistics, for will also be presented. 相似文献
20.
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