437 research outputs found
Balancing lists: a proof pearl
Starting with an algorithm to turn lists into full trees which uses
non-obvious invariants and partial functions, we progressively encode the
invariants in the types of the data, removing most of the burden of a
correctness proof.
The invariants are encoded using non-uniform inductive types which parallel
numerical representations in a style advertised by Okasaki, and a small amount
of dependent types.Comment: To appear in proceedings of Interactive Theorem Proving (2014
Nonsingular instantons for the creation of open universes
We show that the instability of the singular Vilenkin instanton describing
the creation of an open universe can be avoided using, instead of a minimally
coupled scalar field, an axionic massless scalar field which gives rise to the
Giddings-Strominger instanton. However, if we replace the singularity of the
Hawking Turok instanton for an axionic wormhole some interpretational and
technical difficulties would appear which can be overcome by introducing a
positive cosmological constant in the action. This would make the instanton
finite and free constant in the action. This would make the instanton finite
and free from any instabilities.Comment: 8 pages, RevTex. A new section on the instantonic global structure
and a figure have been added. To appear in Phys. Rev.
On reaction thresholds in doubly special relativity
Two theories of special relativity with an additional invariant scale,
"doubly special relativity" (DSR), are tested with calculations of particle
process kinematics. Using the Judes-Visser modified conservation laws,
thresholds are studied in both theories. In contrast to some linear
approximations, which allow for particle processes forbidden in special
relativity, both the Amelino-Camelia and Maguejo-Smolin frameworks allow no
additional processes. To first order, the Amelino-Camelia framework thresholds
are lowered and the Maguejo-Smolin framework thresholds may be raised or
lowered.Comment: 13 pages,v3 added comments regarding the assumption of composite
particles,minor wording changes, version to be publishe
Global Fluctuation Spectra in Big Crunch/Big Bang String Vacua
We study Big Crunch/Big Bang cosmologies that correspond to exact world-sheet
superconformal field theories of type II strings. The string theory spacetime
contains a Big Crunch and a Big Bang cosmology, as well as additional
``whisker'' asymptotic and intermediate regions. Within the context of free
string theory, we compute, unambiguously, the scalar fluctuation spectrum in
all regions of spacetime. Generically, the Big Crunch fluctuation spectrum is
altered while passing through the bounce singularity. The change in the
spectrum is characterized by a function , which is momentum and
time-dependent. We compute explicitly and demonstrate that it arises
from the whisker regions. The whiskers are also shown to lead to
``entanglement'' entropy in the Big Bang region. Finally, in the Milne orbifold
limit of our superconformal vacua, we show that and, hence, the
fluctuation spectrum is unaltered by the Big Crunch/Big Bang singularity. We
comment on, but do not attempt to resolve, subtleties related to gravitational
backreaction and light winding modes when interactions are taken into account.Comment: 68 pages, 1 figure; typos correcte
Charged AdS Black Holes and Catastrophic Holography
We compute the properties of a class of charged black holes in anti-de Sitter
space-time, in diverse dimensions. These black holes are solutions of
consistent Einstein-Maxwell truncations of gauged supergravities, which are
shown to arise from the inclusion of rotation in the transverse space. We
uncover rich thermodynamic phase structures for these systems, which display
classic critical phenomena, including structures isomorphic to the van der
Waals-Maxwell liquid-gas system. In that case, the phases are controlled by the
universal `cusp' and `swallowtail' shapes familiar from catastrophe theory. All
of the thermodynamics is consistent with field theory interpretations via
holography, where the dual field theories can sometimes be found on the world
volumes of coincident rotating branes.Comment: 19 pages, revtex, psfig, 6 multicomponent figures, typos, references
and a few remarks have been repaired, and adde
Dark mammoth trunks in the merging galaxy NGC 1316 and a mechanism of cosmic double helices
NGC 1316 is a giant, elliptical galaxy containing a complex network of dark,
dust features. The morphology of these features has been examined in some
detail using a Hubble Space Telescope, Advanced Camera for Surveys image. It is
found that most of the features are constituted of long filaments. There also
exist a great number of dark structures protruding inwards from the filaments.
Many of these structures are strikingly similar to elephant trunks in H II
regions in the Milky Way Galaxy, although much larger. The structures, termed
mammoth trunks, generally are filamentary and often have shapes resembling the
letters V or Y. In some of the mammoth trunks the stem of the Y can be resolved
into two or more filaments, many of which showing signs of being intertwined. A
model of the mammoth trunks, related to a recent theory of elephant trunks, is
proposed. Based on magnetized filaments, the model is capable of giving an
account of the various shapes of the mammoth trunks observed, including the
twined structures.Comment: Accepted for publication in Astrophysics & Space Scienc
Hawking Temperature in Taub-NUT (A)dS spaces via the Generalized Uncertainty Principle
Using the extended forms of the Heisenberg uncertainty principle from string
theory and the quantum gravity theory, we drived Hawking temperature of a
Taub-Nut-(A)dS black hole. In spite of their distinctive natures such as
asymptotically locally flat and breakdown of the area theorem of the horizon
for the black holes, we show that the corrections to Hawking temperature by the
generalized versions of the the Heisenberg uncertainty principle increases like
the Schwarzschild-(A)dS black hole and give the reason why the Taub-Nut-(A)dS
metric may have AdS/CFT dual picture.Comment: version published in General Relativity and Gravitatio
Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions
We find all the higher dimensional solutions of the Einstein-Maxwell theory
that are the topological product of two manifolds of constant curvature. These
solutions include the higher dimensional Nariai, Bertotti-Robinson and
anti-Nariai solutions, and the anti-de Sitter Bertotti-Robinson solutions with
toroidal and hyperbolic topology (Plebanski-Hacyan solutions). We give explicit
results for any dimension D>3. These solutions are generated from the
appropriate extremal limits of the higher dimensional near-extreme black holes
in a de Sitter, and anti-de Sitter backgrounds. Thus, we also find the mass and
the charge parameters of the higher dimensional extreme black holes as a
function of the radius of the degenerate horizon.Comment: 10 pages, 11 figures, RevTeX4. References added. Published versio
Detecting Microscopic Black Holes with Neutrino Telescopes
If spacetime has more than four dimensions, ultra-high energy cosmic rays may
create microscopic black holes. Black holes created by cosmic neutrinos in the
Earth will evaporate, and the resulting hadronic showers, muons, and taus may
be detected in neutrino telescopes below the Earth's surface. We simulate such
events in detail and consider black hole cross sections with and without an
exponential suppression factor. We find observable rates in both cases: for
conservative cosmogenic neutrino fluxes, several black hole events per year are
observable at the IceCube detector; for fluxes at the Waxman-Bahcall bound,
tens of events per year are possible. We also present zenith angle and energy
distributions for all three channels. The ability of neutrino telescopes to
differentiate hadrons, muons, and possibly taus, and to measure these
distributions provides a unique opportunity to identify black holes, to
experimentally constrain the form of black hole production cross sections, and
to study Hawking evaporation.Comment: 20 pages, 9 figure
Black Holes from Cosmic Rays: Probes of Extra Dimensions and New Limits on TeV-Scale Gravity
If extra spacetime dimensions and low-scale gravity exist, black holes will
be produced in observable collisions of elementary particles. For the next
several years, ultra-high energy cosmic rays provide the most promising window
on this phenomenon. In particular, cosmic neutrinos can produce black holes
deep in the Earth's atmosphere, leading to quasi-horizontal giant air showers.
We determine the sensitivity of cosmic ray detectors to black hole production
and compare the results to other probes of extra dimensions. With n \ge 4 extra
dimensions, current bounds on deeply penetrating showers from AGASA already
provide the most stringent bound on low-scale gravity, requiring a fundamental
Planck scale M_D > 1.3 - 1.8 TeV. The Auger Observatory will probe M_D as large
as 4 TeV and may observe on the order of a hundred black holes in 5 years. We
also consider the implications of angular momentum and possible exponentially
suppressed parton cross sections; including these effects, large black hole
rates are still possible. Finally, we demonstrate that even if only a few black
hole events are observed, a standard model interpretation may be excluded by
comparison with Earth-skimming neutrino rates.Comment: 30 pages, 18 figures; v2: discussion of gravitational infall, AGASA
and Fly's Eye comparison added; v3: Earth-skimming results modified and
strengthened, published versio
- …