318 research outputs found
Cosmological Models with Shear and Rotation
Cosmological models involving shear and rotation are considered, first in the
General Relat ivistic and then in the Newtonian framework with the aim of
investigating singularities in them by using numerical and analytical
techniques. The dynamics of these rotating models ar e studied. It is shown
that singularities are unavoidable in such models and that the centr ifugal
force arising due to rotation can never overcome the gravitational and shearing
forc e over a length of time.Comment: 17 pages, 6 figures Journal Ref: J. Astrophys. Astr. (1999) 20, 79-8
String Supported Wormhole Spacetimes and Causality Violations
We construct a static axisymmetric wormhole from the gravitational field of
two Schwarzschild particles which are kept in equilibrium by strings (ropes)
extending to infinity. The wormhole is obtained by matching two
three-dimensional timelike surfaces surrounding each of the particles and thus
spacetime becomes non-simply connected. Although the matching will not be exact
in general it is possible to make the error arbitrarily small by assuming that
the distance between the particles is much larger than the radius of the
wormhole mouths. Whenever the masses of the two wormhole mouths are different,
causality violating effects will occur.Comment: 12 pages, LaTeX, 1 figur
Josephson Junctions defined by a Nano-Plough
We define superconducting constrictions by ploughing a deposited Aluminum
film with a scanning probe microscope. The microscope tip is modified by
electron beam deposition to form a nano-plough of diamond-like hardness, what
allows the definition of highly transparent Josephson junctions. Additionally a
dc-SQUID is fabricated to verify appropriate functioning of the junctions. The
devices are easily integrated in mesoscopic devices as local radiation sources
and can be used as tunable on-chip millimeter wave sources
An exterior for the G\"{o}del spacetime
We match the vacuum, stationary, cylindrically symmetric solution of
Einstein's field equations with , in a form recently given by Santos,
as an exterior to an infinite cylinder of dust cut out of a G\"{o}del universe.
There are three cases, depending on the radius of the cylinder. Closed timelike
curves are present in the exteriors of some of the solutions. There is a
considerable similarity between the spacetimes investigated here and those of
van Stockum referring to an infinite cylinder of rotating dust matched to
vacuum, with .Comment: 11 pages, LaTeX 2.09, no figures. Submitted to Classical and Quantum
Gravit
On certain relationships between cosmological observables in the Einstein-Cartan gravity
We show that in the Einstein-Cartan gravity it is possible to obtain a
relation between Hubble's expansion and the global rotation (vorticity) of the
Universe. Gravitational coupling can be reduced to dimensionless quantity of
order unity, fixing the scalar mass density and the resulting negative
cosmological constant at spacelike infinity. Current estimates of the expansion
and rotation (see also astro-ph/9703082) of the Universe favour the massive
spinning particles as candidate particles for cold and hot dark matter. Nodland
and Ralston vorticity (Phys. Rev. Lett. 78 (1997) 3043) overestimates the value
favoured by the Einstein-Cartan gravity for three orders of magnitude.Comment: 7 pages, LaTeX styl
Gentzen’s Original Consistency Proof and the Bar Theorem
in December after receiving criticism and, in particular, the criticism that the proof used the Fan Theorem, a criticism that, as the references just cited seem to indicate, Bernays endorsed or initiated at the time but later rejected. That particular criticism is transparently false, but the argument of the paper remains nevertheless invalid from a constructive standpoint. In a letter to Bernays dated November 4, 1935, Gentzen protested this evaluation; but then, in another letter to him dated December 11, 1935, he admits that the “critical inference in my consistency proof is defective. ” The defect in question involves the application of proof by induction to certain trees, the ‘reduction trees ’ for sequents (see below and §1), of which it is only given that they are well-founded. No doubt because of his desire to reason ‘finitistically’, Gentzen nowhere in his paper explicitly speaks of reduction trees, only of reduction rules that would generate such trees; but the requirement of well-foundedness, that every path taken in accordance with the rule terminates, of course makes implicit reference to the tree. Gentzen attempted to avoid th
Takeuti's Well-Ordering Proof: Finitistically Fine?
If it could be shown that one of Gentzen's consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert's program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen's second proof can be finitistically justified. In particular, the focus is on Takeuti's purportedly finitistically acceptable proof of the well-ordering of ordinal notations in Cantor normal form.
The paper begins with a historically informed discussion of finitism and its limits, before introducing Gentzen and Takeuti's respective proofs. The rest of the paper is dedicated to investigating the finitistic acceptability of Takeuti's proof, including a small but important fix to that proof. That discussion strongly suggests that there is a philosophically interesting finitist standpoint that Takeuti's proof, and therefore Gentzen's proof, conforms to
The lightcone of G\"odel-like spacetimes
A study of the lightcone of the G\"odel universe is extended to the so-called
G\"odel-like spacetimes. This family of highly symmetric 4-D Lorentzian spaces
is defined by metrics of the form ,
together with the requirement of spacetime homogeneity, and includes the
G\"odel metric. The quasi-periodic refocussing of cone generators with
startling lens properties, discovered by Ozsv\'{a}th and Sch\"ucking for the
lightcone of a plane gravitational wave and also found in the G\"odel universe,
is a feature of the whole G\"odel family. We discuss geometrical properties of
caustics and show that (a) the focal surfaces are two-dimensional null surfaces
generated by non-geodesic null curves and (b) intrinsic differential invariants
of the cone attain finite values at caustic subsets.Comment: 19 pages, 1 figur
Ringholes and closed timelike curves
It is shown that in a classical spacetime with multiply connected space
slices having the topology of a torus, closed timelike curves are also formed.
We call these spacetime ringholes. Two regions on the torus surface can be
distinguished which are separated by angular horizons. On one of such regions
(that which surrounds the maximum circumference of the torus) everything
happens like in spherical wormholes, but the other region (the rest of the
torus surface), while still possessing a chronology horizon and non-chronal
region, behaves like a coverging, rather than diverging, lens and corresponds
to an energy density which is always positive for large speeds at or near the
throat. It is speculated that a ringhole could be converted into a time machine
to perform time travels by an observer who would never encounter any matter
that violates the classical averaged weak energy condition. Based on a
calculation of vacuum fluctuations, it is also seen that the angular horizons
can prevent the emergence of quantum instabilities near the throat.Comment: 11 pages, RevTex, 4 figures available upon reques
Programmability of Chemical Reaction Networks
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior
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