共查询到20条相似文献,搜索用时 31 毫秒
1.
E. Minguzzi 《Communications in Mathematical Physics》2009,290(1):239-248
It is proven that K-causality coincides with stable causality, and that in a K-causal spacetime the relation K
+ coincides with the Seifert’s relation. As a consequence the causal relation “the spacetime is strongly causal and the closure
of the causal relation is transitive” stays between stable causality and causal continuity. 相似文献
2.
Ioannis Raptis 《International Journal of Theoretical Physics》2006,45(1):79-128
A ‘resolution’ of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and, in extenso, Differential Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machinery of Abstract Differential Geometry (ADG) is employed. As in previous works [Mallios, A. and Raptis, I. (2001). Finitary spacetime sheaves of quantum causal sets: Curving quantum causality. International Journal of Theoretical Physics, 40, 1885 [gr-qc/0102097]; Mallios, A. and Raptis, I. (2002). Finitary Čech-de Rham cohomology. International Journal of Theoretical Physics, 41, 1857 [gr-qc/0110033]; Mallios, A. and Raptis, I. (2003). Finitary, causal and quantal vacuum Einstein gravity. International Journal of Theoretical Physics 42, 1479 [gr-qc/0209048]], which this paper continues, the starting point for the present application of ADG is Sorkin's finitary (:locally finite) poset (:partially ordered set) substitutes of continuous manifolds in their Gel'fand-dual picture in terms of discrete differential incidence algebras and the finitary spacetime sheaves thereof. It is shown that the Einstein equations hold not only at the finitary poset level of ‘discrete events,’ but also at a suitable ‘classical spacetime continuum limit’ of the said finitary sheaves and the associated differential triads that they define ADG-theoretically. The upshot of this is two-fold: On the one hand, the field equations are seen to hold when only finitely many events or ‘degrees of freedom’ of the gravitational field are involved, so that no infinity or uncontrollable divergence of the latter arises at all in our inherently finitistic-algebraic scenario. On the other hand, the law of gravity—still modelled in ADG by a differential equation proper—does not break down in any (differential geometric) sense in the vicinity of the locus of the point-mass as it is traditionally maintained in the usual manifold-based analysis of spacetime singularities in General Relativity (GR). At the end, some brief remarks are made on the potential import of ADG-theoretic ideas in developing a genuinely background-independent Quantum Gravity (QG). A brief comparison between the ‘resolution’ proposed here and a recent resolution of the inner Schwarzschild singularity by Loop QG means concludes the paper.
PACS numbers: 04.60.−m, 04.20.Gz, 04.20.−q 相似文献
3.
Hristu Culetu 《Central European Journal of Physics》2008,6(2):317-320
We take a null hypersurface (causal horizon) generated by a congruence of null geodesics as the boundary of the Doran-Lobo-Crawford
spacetime to be the place where the Brown-York quasilocal energy is located. The components of the outer and inner stress
tensors are computed and shown to depend on time and on the impact parameter b of the test-particle trajectory. The spacetime is a solution of Einstein’s equations with an anisotropic fluid as source.
The surface energy density σ on the boundary is given by the same expression as that obtained previously for the energy stored on a Rindler horizon. For
time intervals long compared to b (when the stretched horizon tends to the causal one), the components of the stress tensors become constant.
相似文献
4.
P. Yodzis 《General Relativity and Gravitation》1973,4(4):299-307
It is shown that ‘changes of topology’ (of spacelike sections) in the spacetime of classical general relativity are consistent
with the following requirements: (i) stable causality, (ii) future causal geodesic completeness, and (iii) finite, positive
energy density. This amounts to showing that the framework of classical general relativity encompasses ‘changes of topology’. 相似文献
5.
A P Balachandran 《Pramana》2001,56(2-3):223-237
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators
are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major
axiom in quantum physics than those formulated for example in Dirac’s ‘quantum mechanics’, then a quantum physicist would
not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with
smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and
with further refinements of the axiom, its C
K - and C
--structures) can be reconstructed using Gel’fand-Naimark theory and its extensions. Classical topology is an attribute of
only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less
differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating
these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental
issues concerning the role of time in quantum physics are also addressed. 相似文献
6.
J. Dieckmann 《General Relativity and Gravitation》1988,20(9):859-867
It is shown that on every spacetime there is a finite Borel measure such that open sets have positive measure and the topological boundary of the chronological past/future of every point has measure zero. Using this measure volume, functions are defined. It is shown that they are semicontinuous, and the set of points at which they are discontinuous is a union of nullgeodesics. The following causality conditions are characterized in terms of their properties: chronological, distinguishing, strongly causal, causally continuous, globally hyperbolic. 相似文献
7.
Recent observations on the quasar absorption spectra supply evidence for the variation of the fine structure constant α. In this paper, we propose another interpretation of the observational data on the quasar absorption spectra: a scenario
with spacetime inhomogeneity and anisotropy. Maybe the spacetime is characterized by the Finsler geometry instead of the Riemann
one. The Finsler geometry admits fewer symmetries than the Riemann geometry does. We investigate the Finslerian geodesic equations
in the Randers spacetime (a special Finsler spacetime). It is found that the cosmological redshift in this spacetime deviates
from the one in general relativity. The modification term to the redshift could be generally revealed as a monopole plus dipole
function of spacetime locations and directions. We suggest that this modification corresponds to the spatial monopole and
dipole of α variation in the quasar absorption spectra. 相似文献
8.
Jacques L. Rubin 《Foundations of Physics》2010,40(2):158-178
On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to
those of space and time, together give a physical justification for the ‘chronometric hypothesis’ of general relativity. Indeed, we show that, with a lack of these latter two ingredients and of this hypothesis, clock paradoxes
exist for which the unparadoxical asymmetry cannot be recovered when using the ‘clock and message functions’ only. These proper times originate from a given conformal structure of the spacetime when ascribing different compatible
projective structures to each Woodhouse particle, and then, each defines a specific Weylian ‘sheaf structure’. In addition, the proper time parameterizations are defined via path-dependent conformal scale factors, which act like sockets
for any kind of physical interaction and also represent the values of the variable associated with the extra dimension. 相似文献
9.
A. M. Vora 《Russian Physics Journal》2006,49(8):834-839
The study of the electrical resistivity of alkali K-based liquid binaries, viz, K
1−x
Na
x, K
1−x
Rb
x, and K
1−x
Cs
x have been made by well recognized model potential. The most recent local field correction functions due to Farid et al. (F)
and Sarkar et al. (S) are used for the first time in the study of electrical resistivity of liquid binary mixtures and found
suitable for such study. The results due to the inclusion of Sarkar et al.’s local field correction function are found superior
to those obtained due to Farid et al.’s local field correction function. The present results compare well the experimental
data.
__________
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 40–44, August, 2006. 相似文献
10.
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emerges from something discrete. 相似文献
11.
Bernard S. Kay Marek J. Radzikowski Robert M. Wald 《Communications in Mathematical Physics》1997,183(3):533-556
We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime,
, with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as ‘past terminal accumulation points’ of the horizon generators. Thus, the theorems
may be interpreted as giving support to Hawking's ‘Chronology Protection Conjecture’, according to which the laws of physics
prevent one from manufacturing a ’time machine‘. Specifically, we prove:
Theorem 1.
There is no extension to
of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base
point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point,
differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes.
Theorem 2.
The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to
a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point
x
in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by
a bounded function in any neighbourhood (in M × M) of (x,x).
In consequence of Theorem 2, quantities such as the renormalized expectation value of φ2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point.
The proof of these theorems relies on the ‘Propagation of Singularities’ theorems of Duistermaat and H?rmander.
Received: 14 March 1996/Accepted: 11 June 1996 相似文献
12.
Leonard P. Gamberg 《Pramana》2009,72(1):55-68
The naive time reversal odd (‘T-odd’) parton distribution and fragmentation functions are explored. We use the spectator model
framework to study flavour dependence of the Boer-Mulders (h
1⊥ ) and Sivers (f
1T⊥) functions as well as the ‘T-even’ but chiral odd function h
1L⊥. These transverse momentum-dependent parton distribution functions are of significance for the analysis of azimuthal asymmetries
in semi-inclusive deep inelastic scattering, as well as for the overall physical understanding of the distribution of transversely
polarized quarks in unpolarized hadrons. In this context we also consider the Collins mechanism and the fragmentation function
H
1⊥. As a by-product of this analysis we calculate the leading twist unpolarized cos(2ϕ) asymmetry, and sin(2ϕ) single spin asymmetry for a longitudinally polarized target in semi-inclusive deep inelastic scattering.
相似文献
13.
Using K-causal relation introduced by Sorkin and Woolgar [1], we generalize results of Garcia-Parrado and Senovilla [2,3]
on causal maps. We also introduce causality conditions with respect to K-causality which are analogous to those in classical
causality theory and prove their inter-relationships. We introduce a new causality condition following the work of Bombelli
and Noldus [4] and show that this condition lies in between global hyperbolicity and causal simplicity. This approach is simpler
and more general as compared to traditional causal approach [5,6] and it has been used by Penrose et al [7] in giving a new proof of positivity of mass theorem. C
0-space-time structures arise in many mathematical and physical situations like conical singularities, discontinuous matter
distributions, phenomena of topology-change in quantum field theory etc.
相似文献
14.
John K. Beem 《Communications in Mathematical Physics》1976,49(2):179-186
Let (M, g) be a causal spacetime. ConditionN will be satisfied if for each compact subsetK ofM there is no future inextendible nonspacelike curve which is totally future imprisoned inK. IfM satisfies conditionN, then wheneverE is an open and relatively compact subset ofM the spacetimeE with the metricg restricted toE is stably causal. Furthermore, there is a conformal factor such that (M, 2
g) is both null and timelike geodesically complete. IfM is an open subset of two dimensional Minkowskian space, thenM is conformal to a geodesically complete spacetime. 相似文献
15.
The folk questions in Lorentzian Geometry which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime (M, g) admits a smooth time function whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting if a spacetime M admits a (continuous) time function t then it admits a smooth (time) function with timelike gradient on all M.The second-named author has been partially supported by a MCyT-FEDER Grant, MTM2004-04934-C04-01.To Professor P.E. Ehrlich, wishing him a continued recovery and good health 相似文献
16.
Michael Grinfeld Philip A. Knight Andrew R. Wade 《Journal of statistical physics》2012,146(2):378-407
We study a class of Markovian systems of N elements taking values in [0,1] that evolve in discrete time t via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspired by variants
of the Bak–Sneppen model of evolution, in which the system represents an evolutionary ‘fitness landscape’ and which is famous
as a simple model displaying self-organized criticality. Our main results are concerned with long-time large-N asymptotics for the general model in which, at each time step, K randomly chosen elements are discarded and replaced by independent U[0,1] variables, where the ranks of the elements to be replaced are chosen, independently at each time step, according to
a distribution κ
N
on {1,2,…,N}
K
. Our main results are that, under appropriate conditions on κ
N
, the system exhibits threshold behavior at s
∗∈[0,1], where s
∗ is a function of κ
N
, and the marginal distribution of a randomly selected element converges to U[s
∗,1] as t→∞ and N→∞. Of this class of models, results in the literature have previously been given for special cases only, namely the ‘mean-field’
or ‘random neighbor’ Bak–Sneppen model. Our proofs avoid the heuristic arguments of some of the previous work and use Foster–Lyapunov
ideas. Our results extend existing results and establish their natural, more general context. We derive some more specialized
results for the particular case where K=2. One of our technical tools is a result on convergence of stationary distributions for families of uniformly ergodic Markov
chains on increasing state-spaces, which may be of independent interest. 相似文献
17.
Fan Zhao 《International Journal of Theoretical Physics》2011,50(11):3509-3514
Taking WKB approximation to solve the scalar field equation in the Schwarzschild black hole spacetime, we can get the classical
momenta. Substituting the classical momenta into state density equation corrected by the modified dispersion relation, we
will obtain the number of quantum states with energy less than ω. Then, it is used to calculate the statistical-mechanical entropy of the scalar field in the Schwarzschild black hole spacetime.
By taking exact method, we obtained the leader term of entropy which is proportional to the event horizon area and correction
terms take the forms of ln A, A
−1ln A, A
−1 and so on. 相似文献
18.
Valter Moretti 《Communications in Mathematical Physics》2008,279(1):31-75
This paper continues the analysis of the quantum states introduced in previous works and determined by the universal asymptotic
structure of four-dimensional asymptotically flat vacuum spacetimes at null infinity M. It is now focused on the quantum state λ
M
, of a massless conformally coupled scalar field propagating in M. λ
M
is “holographically” induced in the bulk by the universal BMS-invariant state λ defined on the future null infinity of M. It is done by means of the correspondence between observables in the bulk and those on the boundary at future null infinity
discussed in previous papers. This induction is possible when some requirements are fulfilled, in particular whenever the
spacetime M and the associated unphysical one, M͂, are globally hyperbolic and M admits future time infinity i
+. λ
M
coincides with Minkowski vacuum if M is Minkowski spacetime. It is now proved that, in the general case of a curved spacetime M, the state λ
M
enjoys the following further remarkable properties:
相似文献
(i) | λ M is invariant under the (unit component of the Lie) group of isometries of the bulk spacetime M. |
(ii) | λ M fulfills a natural energy-positivity condition with respect to every notion of Killing time (if any) in the bulk spacetime M: If M admits a time-like Killing vector, the associated one-parameter group of isometries is represented by a strongly-continuous unitary group in the GNS representation of λ M . The unitary group has positive self-adjoint generator without zero modes in the one-particle space. In this case λ M is a so-called regular ground state. |
(iii) | λ M is (globally) Hadamard in M and thus it can be used as the starting point for the perturbative renormalisation procedure of QFT of in M. |
19.
R. Ferrini G. Guizzetti M. Patrini A. Parisini L. Tarricone B. Valenti 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(4):449-458
In0.49Ga0.51P films, both undoped and doped n- and p-type (up to 1018 cm-3), were grown lattice matched on GaAs substrates, with different miscut angles, by Metal-Organic Vapour Phase Epitaxy (MOVPE)
at different temperatures. The shift of the fundamental gap E0, caused by “ordering effect” was measured as a function of temperature by photoluminescence. The complex refractive index
= n + ik and the dielectric function = ɛ
1 + iɛ
2 at room temperature were determined from 0.01 to 5.5 eV by using complementary data from fast-Fourier-transform far-infrared
(FFT-FIR), dispersive, and ellipsometric spectroscopies. The effect of the native oxide was accounted for and the self-consistency
of the optical functions was checked in the framework of the Kramers-Kronig causality relations. In the restrahlen region
the dielectric function was well fitted by classical Lorentz oscillators; in the transparent region below E0, the refractive index was modelled by a Sellmeier dispersion relation; in the interband region the dielectric function was
well reproduced by analytical lineshapes associated to seven critical points. Thus parametrized analytical expressions were
obtained for the optical functions all over the spectral range, without discontinuities, to be used in the modelling and characterization
of multi-layer structures, also on opaque substrates.
Received 13 December 2001 Published online 25 June 2002 相似文献
20.
Surface plasmon-phonon polaritons (SPPP’s) of types 3 and 4 are investigated in doped anisotropic single crystals of hexagonal
silicon carbide (6H-SiC) in the orientation corresponding to K⊥C and xy⊥C. It is shown that a dispersion dependence of the type-3 SPPP’s bounded by K appears in 6H-SiC when the plasmon frequency increases to ν
p⊥⩾350 cm−1. At ν
p⊥⩾400 cm−1, ν
s(K) exists for type-4 SPPP’s in the frequency range Ω
∥
+
<ν<
⊥
+
. When the concentration of free charge carriers is increased, the dispersion curves are displaced toward higher frequencies.
The conditions for the existence of type-3 and type-4 SPPP’s in 6H-SiC are determined.
Fiz. Tverd. Tela (St. Petersburg) 40, 636–639 (April 1998) 相似文献