Cosmological Constant and Noncommutative Spacetime

We show that the cosmological constant appears as a Lagrange multiplier if nature is described by a canonical noncommutative spacetime. It is thus an arbitrary parameter unrelated to the action and thus to vacuum fluctuations. The noncommutative algebra restricts general coordinate transformations to four-volume preserving noncommutative coordinate transformations. The noncommutative gravitational action is thus an unimodular noncommutative gravity. We show that spacetime noncommutativity provides a very natural justification to an unimodular gravity solution to the cosmological problem. We obtain the right order of magnitude for the critical energy density of the universe if we assume that the scale for spacetime noncommutativity is the Planck scale.Comment: 7 page

Two-dimensional gravity with a dynamical aether

We investigate the two-dimensional behavior of gravity coupled to a dynamical unit timelike vector field, i.e. "Einstein-aether theory". The classical solutions of this theory in two dimensions depend on one coupling constant. When this coupling is positive the only solutions are (i) flat spacetime with constant aether, (ii) de Sitter or anti-de Sitter spacetimes with a uniformly accelerated unit vector invariant under a two-dimensional subgroup of SO(2,1) generated by a boost and a null rotation, and (iii) a non-constant curvature spacetime that has no Killing symmetries and contains singularities. In this case the sign of the curvature is determined by whether the coupling is less or greater than one. When instead the coupling is negative only solutions (i) and (iii) are present. This classical study of the behavior of Einstein-aether theory in 1+1 dimensions may provide a starting point for further investigations into semiclassical and fully quantum toy models of quantum gravity with a dynamical preferred frame.Comment: 11 pages, 4 figure

Action Principle for the Generalized Harmonic Formulation of General Relativity

An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general relativity has been proposed recently by Bona, Bona--Casas and Palenzuela (BBP). The relationship between the generalized harmonic action and the BBP action is discussed in detail.Comment: This version is contains more thorough presentations and discussions of the key results. To be published in PRD. (8 pages, no figures

Field equations from a surface term

As is well known, in order for the Einstein--Hilbert action to have a well defined variation, and therefore to be used for deriving field equation through the stationary action principle, it has to be amended by the addition of a suitable boundary term. It has recently been claimed that, if one constructs an action by adding this term to the matter action, the Einstein field equations can be derived by requiring this action to be invariant under active transformations which are normal to a null boundary. In this paper we re-examine this approach both for the case of pure gravity and in the presence of matter. We show that in the first case this procedure holds for more general actions than the Einstein-Hilbert one and trace the basis of this remarkable attribute. However, it is also pointed out the when matter is rigorously considered the approach breaks down. The reasons for that are thoroughly discussed.Comment: Typos corrected, minor changes to match published versio

Post-Newtonian Approximation in Maxwell-Like Form

The equations of the linearized first post-Newtonian approximation to general relativity are often written in "gravitoelectromagnetic" Maxwell-like form, since that facilitates physical intuition. Damour, Soffel and Xu (DSX) (as a side issue in their complex but elegant papers on relativistic celestial mechanics) have expressed the first post-Newtonian approximation, including all nonlinearities, in Maxwell-like form. This paper summarizes that DSX Maxwell-like formalism (which is not easily extracted from their celestial mechanics papers), and then extends it to include the post-Newtonian (Landau-Lifshitz-based) gravitational momentum density, momentum flux (i.e. gravitational stress tensor) and law of momentum conservation in Maxwell-like form. The authors and their colleagues have found these Maxwell-like momentum tools useful for developing physical intuition into numerical-relativity simulations of compact binaries with spin.Comment: v4: Revised for resubmission to Phys Rev D, 6 pages. v3: Reformulated in terms of DSX papers. Submitted to Phys Rev D, 6 pages. v2: Added references. Changed definitions & convention

Empirical constraints on vacuum decay in the stringy landscape

It is generally considered as self evident that the lifetime of our vacuum in the landscape of string theory cannot be much shorter than the current age of the universe. Here I show why this lower limit is invalid. A certain type of ``parallel universes'' is a necessary consequence of the string-landscape dynamics and might well allow us to ``survive'' vacuum decay. As a consequence our stringy vacuum's lifetime is empirically unconstrained and could be very short. Based on this counter-intuitive insight I propose a novel type of laboratory experiment that searches for an apparent violation of the quantum-mechanical Born rule by gravitational effects on vacuum decay. If the lifetime of our vacuum should turn out to be shorter than 6 x 10^{-13} seconds such an experiment is sufficiently sensitive to determine its value with state-of-the-art equipment.Comment: 13 pages, 2 figures, proposes a laboratory experimen

Generalized Mean Field Approach to a Resonant Bose-Fermi Mixture

We formulate a generalized mean-field theory of a mixture of fermionic and bosonic atoms, in which the fermion-boson interaction can be controlled by a Feshbach resonance. The theory correctly accounts for molecular binding energies of the molecules in the two-body limit, in contrast to the most straightforward mean-field theory. Using this theory, we discuss the equilibrium properties of fermionic molecules created from atom pairs in the gas. We also address the formation of molecules when the magnetic field is ramped across the resonance, and present a simple Landau-Zener result for this process.Comment: 35 page

HERMIES-3: A step toward autonomous mobility, manipulation, and perception

HERMIES-III is an autonomous robot comprised of a seven degree-of-freedom (DOF) manipulator designed for human scale tasks, a laser range finder, a sonar array, an omni-directional wheel-driven chassis, multiple cameras, and a dual computer system containing a 16-node hypercube expandable to 128 nodes. The current experimental program involves performance of human-scale tasks (e.g., valve manipulation, use of tools), integration of a dexterous manipulator and platform motion in geometrically complex environments, and effective use of multiple cooperating robots (HERMIES-IIB and HERMIES-III). The environment in which the robots operate has been designed to include multiple valves, pipes, meters, obstacles on the floor, valves occluded from view, and multiple paths of differing navigation complexity. The ongoing research program supports the development of autonomous capability for HERMIES-IIB and III to perform complex navigation and manipulation under time constraints, while dealing with imprecise sensory information

Indistinguishable Particles in Quantum Mechanics: An Introduction

In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states.Comment: To appear in Contemp. Phy

A precise response function for the magnetic component of Gravitational Waves in Scalar-Tensor Gravity

The important issue of the magnetic component of gravitational waves (GWs) has been considered in various papers in the literature. From such analyses, it resulted that such a magnetic component becomes particularly important in the high frequency portion of the frequency range of ground based interferometers for GWs which arises from standard General Theory of Relativity (GTR). Recently, such a magnetic component has been extended to GWs arising from Scalar-Tensor Gravity (STG) too. After a review of some important issues on GWs in STG, in this paper we re-analyse the magnetic component in the framework of STG from a different point of view, by correcting an error in a previous paper and by releasing a more precise response function. In this way, we also show that if one neglects the magnetic contribution considering only the low-frequency approximation of the electric contribution, an important part of the signal could be, in principle, lost. The determination of a more precise response function for the magnetic contribution is important also in the framework of the possibility to distinguish other gravitational theories from GTR. At the end of the paper an expansion of the main results is also shown in order to recall the presence of the magnetic component in GRT too.Comment: Accepted for publication in Physical Review D, to be published during 2011. 36 pages, in this second version typos have been corrected and references have been update