3,745 research outputs found
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
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