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.

The linear growth rate of structure in Parametrized Post Friedmannian Universes

A possible solution to the dark energy problem is that Einstein's theory of general relativity is modified. A suite of models have been proposed that, in general, are unable to predict the correct amount of large scale structure in the distribution of galaxies or anisotropies in the Cosmic Microwave Background. It has been argued, however, that it should be possible to constrain a general class of theories of modified gravity by focusing on properties such as the growing mode, gravitational slip and the effective, time varying Newton's constant. We show that assuming certain physical requirements such as stability, metricity and gauge invariance, it is possible to come up with consistency conditions between these various parameters. In this paper we focus on theories which have, at most, 2nd derivatives in the metric variables and find restrictions that shed light on current and future experimental constraints without having to resort to a (as yet unknown) complete theory of modified gravity. We claim that future measurements of the growth of structure on small scales (i.e. from 1-200 h^{-1} Mpc) may lead to tight constraints on both dark energy and modified theories of gravity.Comment: 15 Pages, 11 Figure

Pulsation of Spherically Symmetric Systems in General Relativity

The pulsation equations for spherically symmetric black hole and soliton solutions are brought into a standard form. The formulae apply to a large class of field theoretical matter models and can easily be worked out for specific examples. The close relation to the energy principle in terms of the second variation of the Schwarzschild mass is also established. The use of the general expressions is illustrated for the Einstein-Yang-Mills and the Einstein-Skyrme system.Comment: 21 pages, latex, no figure

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

Gravitomagnetism, clocks and geometry

New techniques to evaluate the clock effect using light are described. These are based on the flatness of the cylindrical surface containing the world lines of the rays constrained to move on circular trajectories about a spinning mass. The effect of the angular momentum of the source is manifested in the fact that inertial observers must be replaced by local non rotating observers. Starting from this an exact formula for circular trajectories is found. Numerical estimates for the Earth environment show that light would be a better probe than actual clocks to evidence the angular momentum influence. The advantages of light in connection with some principle experiments are shortly reviewed.Comment: TCI Latex, 12 pages, 2 figures. To appear in European Journal of Physic

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

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

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