668 research outputs found
Godel-type space-time metrics
A simple group theoretic derivation is given of the family of space-time
metrics with isometry group SO(2,1) X SO(2) X R first described by Godel, of
which the Godel stationary cosmological solution is the member with a
perfect-fluid stress-energy tensor. Other members of the family are shown to be
interpretable as cosmological solutions with a electrically charged perfect
fluid and a magnetic field.Comment: Heavly rewritten respect to the orginal version, corrected some typos
due to files transfer in the last submitted versio
Godel Type Metrics in Randall Sundrum Model
Anisotropic cosmological models such as the G\"{o}del universe and its
extensions - G\"{o}del type solutions, are embedded on a visible 3-brane in the
Randall-Sundrum 1 model. The size of the extra dimension is stabilized by
tuning the rotation parameter to a very small value so that hierarchy problem
can be solved. A limiting case also yields the Randall-Sundrum 2 model. The
rotation parameter on the visible brane turns out to be of order ,
which implies that visible brane essentially lacks rotation.Comment: 10 pages, typos corrected and references adde
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
Essential Incompleteness of Arithmetic Verified by Coq
A constructive proof of the Goedel-Rosser incompleteness theorem has been
completed using the Coq proof assistant. Some theory of classical first-order
logic over an arbitrary language is formalized. A development of primitive
recursive functions is given, and all primitive recursive functions are proved
to be representable in a weak axiom system. Formulas and proofs are encoded as
natural numbers, and functions operating on these codes are proved to be
primitive recursive. The weak axiom system is proved to be essentially
incomplete. In particular, Peano arithmetic is proved to be consistent in Coq's
type theory and therefore is incomplete.Comment: This paper is part of the proceedings of the 18th International
Conference on Theorem Proving in Higher Order Logics (TPHOLs 2005). For the
associated Coq source files see the TeX sources, or see
<http://r6.ca/Goedel20050512.tar.gz
On the Concept of a Notational Variant
In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic
Vacuum energy and Universe in special relativity
The problem of cosmological constant and vacuum energy is usually thought of
as the subject of general relativity. However, the vacuum energy is important
for the Universe even in the absence of gravity, i.e. in the case when the
Newton constant G is exactly zero, G=0. We discuss the response of the vacuum
energy to the perturbations of the quantum vacuum in special relativity, and
find that as in general relativity the vacuum energy density is on the order of
the energy density of matter. In general relativity, the dependence of the
vacuum energy on the equation of state of matter does not contain G, and thus
is valid in the limit when G tends to zero. However, the result obtained for
the vacuum energy in the world without gravity, i.e. when G=0 exactly, is
different.Comment: LaTeX file, 7 pages, no figures, to appear in JETP Letters, reference
is adde
On closed rotating worlds
A new solution for the stationary closed world with rigid rotation is
obtained for the spinning fluid source. It is found that the spin and vorticity
are locally balanced. This model qualitatively shows that the local rotation of
the cosmological matter can be indeed related to the global cosmic vorticity,
provided the total angular momentum of the closed world is vanishing.Comment: 10 pages, Revtex, to appear in Phys. Rev. D6
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
Spacetime could be simultaneously continuous and discrete in the same way that information can
There are competing schools of thought about the question of whether
spacetime is fundamentally either continuous or discrete. Here, we consider the
possibility that spacetime could be simultaneously continuous and discrete, in
the same mathematical way that information can be simultaneously continuous and
discrete. The equivalence of continuous and discrete information, which is of
key importance in information theory, is established by Shannon sampling
theory: of any bandlimited signal it suffices to record discrete samples to be
able to perfectly reconstruct it everywhere, if the samples are taken at a rate
of at least twice the bandlimit. It is known that physical fields on generic
curved spaces obey a sampling theorem if they possess an ultraviolet cutoff.
Most recently, methods of spectral geometry have been employed to show that
also the very shape of a curved space (i.e., of a Riemannian manifold) can be
discretely sampled and then reconstructed up to the cutoff scale. Here, we
develop these results further, and we here also consider the generalization to
curved spacetimes, i.e., to Lorentzian manifolds
Set Theory and its Place in the Foundations of Mathematics:a new look at an old question
This paper reviews the claims of several main-stream candidates to be the foundations of mathematics, including set theory. The review concludes that at this level of mathematical knowledge it would be very unreasonable to settle with any one of these foundations and that the only reasonable choice is a pluralist one
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