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 $\Delta$, which is momentum and time-dependent. We compute $\Delta$ 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 $\Delta\to 1$ 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

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

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

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