Reflections on a Measurement of the Gravitational Constant Using a Beam Balance and 13 Tons of Mercury

In 2006, a final result of a measurement of the gravitational constant $G$ performed by researchers at the University of Z\"urich was published. A value of G=6.674\,252(122)\times 10^{-11}\,\mbox{m}^3\,\mbox{kg}^{-1}\,\mbox{s}^{-2} was obtained after an experimental effort that lasted over one decade. Here, we briefly summarize the measurement and discuss the strengths and weaknesses of this approach.Comment: 13 pages, 5 figures accepted for publication in Phil. Trans. R. Soc.

An Ontology for Submarine Feature Representation on Charts

A landform is a subjective individuation of a part of a terrain. Landform recognition is a difficult task because its definition usually relies on a qualitative and fuzzy description. Achieving automatic recognition of landforms requires a formal definition of the landforms properties and their modelling. In the maritime domain, the International Hydrographic Organisation published a standard terminology of undersea feature names which formalises a set of definition mainly for naming and communication purpose. This terminology is here used as a starting point for the definition of an ontology of undersea features and their automatic classification from a terrain model. First, an ontology of undersea features is built. The ontology is composed of an application domain ontology describing the main properties and relationships between features and a representation ontology deals with representation on a chart where features are portrayed by soundings and isobaths. A database model was generated from the ontology. Geometrical properties describing the feature shape are computed from soundings and isobaths and are used for feature classification. An example of automatic classification on a nautical chart is presented and results and on-going research are discussed

Soliton and black hole solutions of su(N) Einstein-Yang-Mills theory in anti-de Sitter space

We present new soliton and hairy black hole solutions of su(N) Einstein-Yang-Mills theory in asymptotically anti-de Sitter space. These solutions are described by N+1 independent parameters, and have N-1 gauge field degrees of freedom. We examine the space of solutions in detail for su(3) and su(4) solitons and black holes. If the magnitude of the cosmological constant is sufficiently large, we find solutions where all the gauge field functions have no zeros. These solutions are of particular interest because we anticipate that at least some of them will be linearly stable.Comment: 15 pages, 20 figures, minor changes, accepted for publication in Physical Review

Effect of Peculiar Motion in Weak Lensing

We study the effect of peculiar motion in weak gravitational lensing. We derive a fully relativistic formula for the cosmic shear and the convergence in a perturbed Friedmann Universe. We find a new contribution related to galaxies peculiar velocity. This contribution does not affect cosmic shear in a measurable way, since it is of second order in the velocity. However, its effect on the convergence (and consequently on the magnification, which is a measurable quantity) is important, especially for redshifts z < 1. As a consequence, peculiar motion modifies also the relation between the shear and the convergence.Comment: 11 pages, 7 figures; v2: discussion on the reduced shear added (5.C), additional references, version accepted in PRD; v3: mistakes corrected in eqs. (26), (31), (33) and (44); results unchange

A Measurement of Newton's Gravitational Constant

A precision measurement of the gravitational constant $G$ has been made using a beam balance. Special attention has been given to determining the calibration, the effect of a possible nonlinearity of the balance and the zero-point variation of the balance. The equipment, the measurements and the analysis are described in detail. The value obtained for G is 6.674252(109)(54) 10^{-11} m3 kg-1 s-2. The relative statistical and systematic uncertainties of this result are 16.3 10^{-6} and 8.1 10^{-6}, respectively.Comment: 26 pages, 20 figures, Accepted for publication by Phys. Rev.

Angular momentum effects in Michelson-Morley type experiments

The effect of the angular momentum density of a gravitational source on the times of flight of light rays in an interferometer is analyzed. The calculation is made imagining that the interferometer is at the equator of the gravity source and, as long as possible, the metric, provided it is stationary and axisymmetric, is not approximated. Finally, in order to evaluate the size of the effect in the case of the Earth a weak field approximation is introduced. For laboratory scales and non-geodesic paths the correction turns out to be comparable with the sensitivity expected in gravitational waves interferometric detectors, whereas it drops under the threshold of detectability when using free (geodesic) light rays.Comment: 12 pages, LaTeX; more about the detection technique, references added; accepted for publication in GR

Aspects of hairy black holes in spontaneously-broken Einstein-Yang-Mills systems: Stability analysis and Entropy considerations

We analyze (3+1)-dimensional black-hole space-times in spontaneously broken Yang-Mills gauge theories that have been recently presented as candidates for an evasion of the scalar-no-hair theorem. Although we show that in principle the conditions for the no-hair theorem do not apply to this case, however we prove that the `spirit' of the theorem is not violated, in the sense that there exist instabilities, in both the sphaleron and gravitational sectors. The instability analysis of the sphaleron sector, which was expected to be unstable for topological reasons, is performed by means of a variational method. As shown, there exist modes in this sector that are unstable against linear perturbations. Instabilities exist also in the gravitational sector. A method for counting the gravitational unstable modes, which utilizes a catastrophe-theoretic approach is presented. The r\^ole of the catastrophe functional is played by the mass functional of the black hole. The Higgs vacuum expectation value (v.e.v.) is used as a control parameter, having a critical value beyond which instabilities are turned on. The (stable) Schwarzschild solution is then understood from this point of view. The catastrophe-theory appproach facilitates enormously a universal stability study of non-Abelian black holes, which goes beyond linearized perturbations. Some elementary entropy considerations are also presented...Comment: Latex file, 50 pages, 2 figures (included as PS files at the end: plot1.ps, plot2.ps

Late-time evolution of the Yang-Mills field in the spherically symmetric gravitational collapse

We investigate the late-time evolution of the Yang-Mills field in the self-gravitating backgrounds: Schwarzschild and Reissner-Nordstr\"om spacetimes. The late-time power-law tails develop in the three asymptotic regions: the future timelike infinity, the future null infinity and the black hole horizon. In these two backgrounds, however, the late-time evolution has quantitative and qualitative differences. In the Schwarzschild black hole background, the late-time tails of the Yang-Mills field are the same as those of the neutral massless scalar field with multipole moment l=1. The late-time evolution is dominated by the spacetime curvature. When the background is the Reissner-Nordstr\"om black hole, the late-time tails have not only a smaller power-law exponent, but also an oscillatory factor. The late-time evolution is dominated by the self-interacting term of the Yang-Mills field. The cause responsible for the differences is revealed.Comment: Revtex, 14 pages, no figure

Consistent Group and Coset Reductions of the Bosonic String

Dimensional reductions of pure Einstein gravity on cosets other than tori are inconsistent. The inclusion of specific additional scalar and p-form matter can change the situation. For example, a D-dimensional Einstein-Maxwell-dilaton system, with a specific dilaton coupling, is known to admit a consistent reduction on S^2= SU(2)/U(1), of a sort first envisaged by Pauli. We provide a new understanding, by showing how an S^3=SU(2) group-manifold reduction of (D+1)-dimensional Einstein gravity, of a type first indicated by DeWitt, can be broken into in two steps; a Kaluza-type reduction on U(1) followed by a Pauli-type coset reduction on S^2. More generally, we show that any D-dimensional theory that itself arises as a Kaluza U(1) reduction from (D+1) dimensions admits a consistent Pauli reduction on any coset of the form G/U(1). Extensions to the case G/H are given. Pauli coset reductions of the bosonic string on G= (G\times G)/G are believed to be consistent, and a consistency proof exists for S^3=SO(4)/SO(3). We examine these reductions, and arguments for consistency, in detail. The structures of the theories obtained instead by DeWitt-type group-manifold reductions of the bosonic string are also studied, allowing us to make contact with previous such work in which only singlet scalars are retained. Consistent truncations with two singlet scalars are possible. Intriguingly, despite the fact that these are not supersymmetric models, if the group manifold has dimension 3 or 25 they admit a superpotential formulation, and hence first-order equations yielding domain-wall solutions.Comment: Latex, 5 figures, 45 pages, minor correction

Static Axially Symmetric Einstein-Yang-Mills-Dilaton Solutions: II.Black Hole Solutions

We discuss the new class of static axially symmetric black hole solutions obtained recently in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory. These black hole solutions are asymptotically flat and they possess a regular event horizon. The event horizon is almost spherically symmetric with a slight elongation along the symmetry axis. The energy density of the matter fields is angle-dependent at the horizon. The static axially symmetric black hole solutions satisfy a simple relation between mass, dilaton charge, entropy and temperature. The black hole solutions are characterized by two integers, the winding number $n$ and the node number $k$ of the purely magnetic gauge field. With increasing node number the magnetically neutral black hole solutions form sequences tending to limiting solutions with magnetic charge $n$, corresponding to Einstein-Maxwell-dilaton black hole solutions for finite dilaton coupling constant and to Reissner-Nordstr\o m black hole solutions for vanishing dilaton coupling constant.Comment: 41 pages including 45 postscript figures, RevTex forma