Showing papers on "Gravitation published in 1991"

Nonlinear nature of gravitation and gravitational-wave experiments.

Abstract: It is shown that gravitational waves from astronomical sources have a nonlinear effect on laser interferometer detectors on Earth, an effect which has hitherto been neglected, but which is of the same order of magnitude as the linear effects. The signature of the nonlinear effect is a permanent displacement of test mases after the passage of a wave train.

What Is Observable in Classical and Quantum Gravity

Abstract: The problem of the identification of the observable quantities in quantum gravity (or in any diffeomorphism invariant quantum theory) is considered. The author recalls Einstein's 'hole argument' on the impossibility of a priori identifying spacetime points. He argues that only by explicitly taking into account the physical nature of the bodies that form the reference system and their gravitational interactions one can get well defined gauge-invariant (and 'local') observables and a definition of physical spacetime points. A model is considered in which general relativity is coupled to matter: the matter represents the physical reference system. The gauge-invariant physical observables of this theory are displayed.

The evolution of groups of galaxies in the Press-Schechter formalism

Abstract: The Press-Schechter theory provides a simple analytical description for the evolution of gravitational structure in a hierarchical univers. The original theory is extended in order to focus on the subset regions that will eventually collapse to form cluster of a set mass. The conditional multiplicity function of groups at an epoch with redshift z, given that they are bound into an object of a particular mass at the present epoch, is determined and combined with the present distribution of group masses in order to obtain the joint multiplicity function. An application to the evolution of groups of galaxies is realised.

Celestial mechanics, conformal structures, and gravitational waves.

Abstract: Newton's equations for the motion of $N$ nonrelativistic point particles attracting according to the inverse square law may be cast in the form of equations for null geodesics in a ($3N+2$)-dimensional Lorentzian spacetime which is Ricci flat and admits a covariantly constant null vector. Such a spacetime admits a Bargmann structure and corresponds physically to a plane-fronted gravitational wave (generalized pp wave). Bargmann electromagnetism in five dimensions actually comprises the two distinct Galilean electromagnetic theories pointed out by Le Bellac and L\'evy-Leblond. At the quantum level, the $N$-body Schr\"odinger equation may be cast into the form of a massless wave equation. We exploit the conformal symmetries of such spacetimes to discuss some properties of the Newtonian $N$-body problem, in particular, (i) homographic solutions, (ii) the virial theorem, (iii) Kepler's third law, (iv) the Lagrange-Laplace-Runge-Lenz vector arising from three conformal Killing two-tensors, and (v) the motion under time-dependent inverse-square-law forces whose strength varies inversely as time in a manner originally envisaged by Dirac in his theory of a time-dependent gravitational constant $G(t)$. It is found that the problem can be reduced to one with time-independent inverse-square-law forces for a rescaled position vector and a new time variable. This transformation (Vinti and Lynden-Bell) is shown to arise from a particular conformal transformation of spacetime which preserves the Ricci-flat condition originally pointed out by Brinkmann. We also point out (vi) a Ricci-flat metric representing a system of $N$ nonrelativistic gravitational dyons. Our results for a general time-dependent $G(t)$ are also applicable by suitable reinterpretation to the motion of point particles in an expanding universe. Finally we extend these results to the quantum regime.

Time in quantum gravity: An hypothesis.

Abstract: A solution to the issue of time in quantum gravity is proposed. The hypothesis that time is not defined at the fundamental level (at the Planck scale) is considered. A natural extension of canonical Heisenberg-picture quantum mechanics is defined. It is shown that this extension is well defined and can be used to describe the "non-Schr\"odinger regime," in which a fundamental time variable is not defined. This conclusion rests on a detailed analysis of which quantities are the physical observables of the theory; a main technical result of the paper is the identification of a class of gauge-invariant observables that can describe the (observable) evolution in the absence of a fundamental definition of time. The choice of the scalar product and the interpretation of the wave function are carefully discussed. The physical interpretation of the extreme "no time" quantum gravitational physics is considered.

Self-dual 2-forms and gravity

Abstract: A Palatini-type formulation of gravity coupled to matter and supergravity is given, in which the gravitational variables are a trio of self-dual 2-forms and an SL(2,C) connection. The action is polynomial in all the fields. This framework is shown to be the natural covariantization of Ashtekar's canonical formalism (1988), and is used to find the general vacuum solution of the four initial value constraints associated with spacetime diffeomorphisms in that formalism.

General-relativistic celestial mechanics. I. Method and definition of reference systems.

Abstract: We present a new formalism for treating the general-relativistic celestial mechanics of systems of $N$ arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such $N$-body systems ("external problem"), (ii) the local gravitational structure of each body ("internal problem"), and, (iii) the way the external and the internal problems fit together ("theory of reference systems"). This formalism uses in a complementary manner $N+1$ coordinate charts (or "reference systems"): one "global" chart for describing the overall dynamics of the $N$ bodies, and $N$ "local" charts adapted to the separate description of the structure and environment of each body. The main tool which allows us to develop, in an elegant manner, a constructive theory of these $N+1$ reference systems is a systematic use of a particular "exponential" parametrization of the metric tensor which has the effect of linearizing both the field equations, and the transformation laws under a change of reference system. This linearity allows a treatment of the first post-Newtonian relativistic celestial mechanics which is, from a structural point of view, nearly as simple and transparent as its Newtonian analogue. Our scheme differs from previous attempts in several other respects: the structure of the stress-energy tensor is left completely open; the spatial coordinate grid (in each system) is fixed by algebraic conditions while a convenient "gauge" flexibility is left open in the time coordinate [at the order $\ensuremath{\delta}t=O({c}^{\ensuremath{-}4})$]; the gravitational field locally generated by each body is skeletonized by particular relativistic multipole moments recently introduced by Blanchet and Damour, while the external gravitational field experienced by each body is expanded in terms of a particular new set of relativistic tidal moments. In this first paper we lay the foundations of our formalism, with special emphasis on the definition and properties of the $N$ local reference systems, and on the general structure and transformation properties of the gravitational field. As an illustration of our approach we treat in detail the simple case where each body can, in some approximation, be considered as generating a spherically symmetric gravitational field. This "monopole truncation" leads us to a new (and, in our opinion, improved) derivation of the Lorentz-Droste-Einstein-Infeld-Hoffmann equations of motion. The detailed treatment of the relativistic motion of bodies endowed with arbitrary multipole structure will be the subject of subsequent publications.

Exact scalar field cosmologies

Abstract: The authors consider exact cosmological solutions of the Einstein gravitational equations with a non-interacting combination of a classical scalar field and isotropic radiation as source. They show how a potential function for the scalar field can be found leading to desired volume behaviour of Robertson-Walker universes, and give a number of exact solutions of the coupled equations. These solutions in general do not obey the 'slow-rolling' approximation usually assumed in inflationary universe models.

Topology change in classical and quantum gravity

Abstract: In a first-order formulation, the equations of general relativity remain well defined even in the limit that the metric becomes degenerate. It is shown that there exist smooth solutions to these equations on manifolds in which the topology of space changes. The metric becomes degenerate on a set of measure zero, but the curvature remains bounded. Thus if degenerate metrics play any role in quantum gravity, topology change is unavoidable.

Principles, methods, and application of particle size analysis: Principles and methods of geological particle size analysis

Abstract: Introduction Particle size is a fundamental property of sedimentary materials that may tell us much about their origins and history In particular the dynamical conditions of transport and deposition of the constituent particles of rocks is usually inferred from their size The size distribution is also an essential property for assessing the likely behaviour of granular material under applied fluid or gravitational forces, and gauging the economic utility of bulk materials ranging from foundry sands to china clay Among solid bodies only a sphere has a single characteristic linear dimension Irregular sedimentary particles possess many properties from which several characteristic linear dimensions may be obtained These include a particle's projected area, settling velocity, volume, lengths, and the size of a hole through which it will pass These dimensions are, of course, not equivalent, save in special circumstances (eg, for a sphere), a fact which is generally appreciated but usually overlooked Krumbein & Pettijohn (1938) give a detailed analysis of the properties used as measures of particle size Their book is the reference for all that we shall refer to as “classical” in this chapter There is a huge variety of commercially available instruments, but we have not attempted to list them all (but see the appendix for names and addresses) A concise survey of the state of the market in 1987 was provided by Stanley-Wood (1987a) and a little earlier by Bunville (1984)

A pure spin-connection formulation of gravity

Abstract: A new action principle, in which the only gravitational variables are an SL(2,C) connection and a scalar density, is derived for general relativity (GR) coupled to matter and for supergravity. In this form, GR appears as a non-metric, generally covariant gauge theory, the metric being reconstructed from the other fields in a solution. A similar non-metric action with a real SO(3,1) connection is also derived, however it involves an independent fourth rank tensor field representing the curvature.

The Wave Function of the Universe and p-ADIC Gravity

Abstract: A new approach to the wave function of the universe is suggested. The key idea is to take into account fluctuating number fields and present the wave function in the form of a Euler product. For this purpose we define a p-adic generalization of both classical and quantum gravitational theory. Elements of p-adic differential geometry are described. The action and gravitation field equations over the p-adic number field are investigated. p-adic analogs of some known solutions to the Einstein equations are presented. It follows that in quantum cosmology one should consider summation only over algebraic manifolds. The correspondence principle with the standard approach is considered.

On the non-radial oscillations of a star

Abstract: A complete theory of the non-radial oscillations of a static spherically symmetric distribution of matter, described in terms of an energy density and an isotropic pressure, is developed, ab initio, on the premise that the oscillations are excited by incident gravitational waves. The equations, as formulated, enable the decoupling of the equations governing the perturbations in the metric of the space-time from the equations governing the hydrodynamical variables. This decoupling of the equations reduces the problem of determining the complex characteristic frequencies of the quasi-normal modes of the non-radial oscillations to a problem in the scattering of incident gravitational waves by the curvature of the space-time and the matter content of the source acting as a potential. The present paper is restricted (for the sake of simplicity) to the case when the underlying equation of state is barotropic. The algorism developed for the determination of the quasi-normal modes is directly confirmed by comparison with an independent evaluation by the extant alternative algorism. Both polar and axial perturbations are considered. Dipole oscillations (which do not emit gravitational waves), are also treated as a particularly simple special case. Thus, all aspects of the theory of the non-radial oscillations of stars find a unified treatment in the present approach. The reduction achieved in this paper, besides providing a fresh understanding of known physical problems when formulated in the spirit of general relativity, provides also a basis for an understanding, at a deeper level, of Newtonian theory itself.

Perturbations of the Robertson-Walker space - Multicomponent sources and generalized gravity

Abstract: Cosmological perturbation equations in the Robertson-Walker background space, considering multicomponent fluid sources with interactions between them, are presented. The perturbation equations, applicable to a class of generalized gravity theories with multicomponent fluids and fields as sources, are generalized. Equations are derived from the covariant equations and presented using the raw kinematic variables of the normal frame with an unspecified gauge. In this way, the equations are easily adaptable to various gauge conditions and also to various gauge-invariant formulations. Relations between different gauges and also to the gauge-invariant formulations are explained

Superfluid hydrodynamics in rotating neutron stars. I : Nondissipative equations

Abstract: Newtonian hydrodynamic equations are developed which describe the outer-core regions of neutron stars composed of superfluid neutrons, superconducting protons, and degenerate electrons and muons. The equations include couplings to the gravitational and electromagnetic fields. They also include the effects of rotation and forces due to the elastic properties of the neutron and proton vortices. The set of equations is closed by constructing a model of the total energy density and using it to express the dependent variables in terms of the independent variables. The low-frequency-long-wavelength limit of the equations is determined.

Precollapse Scale Invariance in Gravitational Instability

Abstract: We numerically and analytically investigate the transition to the very nonlinear regime during the gravitational collapse of collisionless matter in an Ω=1 expanding universe. It is found numerically that the formation of halos from isolated and smooth initial overdensities leads to the progressive establishment, complete at the collapse time, of a power-law density profile. The evolutions from various types of initial perturbations are shown to all produce such power laws. The slopes are different, but the scale invariance itself appears quite generic

Smooth static solutions of the Einstein/Yang-Mills equations

Abstract: We consider the Einstein/Yang-Mills equations in 3+1 space time dimensions withSU(2) gauge group and prove rigorously the existence of a globally defined smooth static solution We show that the associated Einstein metric is asymptotically flat and the total mass is finite Thus, for non-abelian gauge fields the Yang-Mills repulsive force can balance the gravitational attractive force and prevent the formation of singularities in spacetime

New tests of the strong equivalence principle using binary-pulsar data.

Abstract: One of the few experimental handles on the nonlinear properties of the gravitational interaction is to test the ``strong equivalence principle,'' i.e., to test whether the ratio ${\mathit{m}}_{\mathrm{gravitational}}$/${\mathit{m}}_{\mathrm{inertial}}$ is 1 for self-gravitating bodies. We point out that existing observational data on the class of small-eccentricity long-orbital-period binary pulsars already provide a limit (namely \ensuremath{\Vert}${\mathit{m}}_{\mathit{g}}$/${\mathit{m}}_{\mathit{i}}$-1\ensuremath{\Vert}1.1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$; 90% C.L.) which goes beyond corresponding solar-system limits in probing strong-gravitational-field effects. Possible observational ways of improving this limit are suggested.

Einstein equivalence principle and the polarization of radio galaxies.

Abstract: The theoretical foundations of metric theories of gravitation rest largely on the Einstein equivalence principle (EEP). Schiff has conjectured that no consistent Lorentz-invariant theory can obey the weak equivalence principle and not obey the EEP. However, a counterexample has been proposed by Ni in a theoretical framework for studying electromagnetism coupled to gravity. Under the assumption that gravitational fields vary smoothly over a Hubble time, we show that Ni's counterexample would lead to a rotation in the plane of polarization of radiation from distant ratio sources

Unimodular theory of gravity and the cosmological constant

Abstract: The unimodular theory of gravity with a constrained determinant gμν is equivalent to general relativity with an arbitrary cosmological constant Λ. Within this framework Λ appears as an integration constant unrelated to any parameters in the Lagrangian. In a quantum theory the state vector of the universe is thus expected to be a superposition of states with different values of Λ. Following Hawking’s argument one concludes that the fully renormalized Λ=0 completely dominates other contributions to the integral over Λ in the vacuum functional. In this scenario of the unimodular theory of gravity the cosmological constant problem is solved. Furthermore, this formulation naturally provides an external (cosmic) time for time ordering of measurements so that the quantum version of the unimodular theory can have a normal ‘‘Schrodinger’’ form of time development, giving a simpler interpretation to the equation of the universe.

Two Lectures on Fermions and Gravity

Abstract: In these two lectures we want to provide information on the behavior of elementary particles in special relativity (SR), such as electrons, protons, or neutrons, in order to get ideas of the underlying principles of the gravitational interaction of fermions. For tangible matter and for the electromagnetic field, Einstein’s gravitational theory, general relativity (GR), describes all phenomena very well and has been verified experimentally with ever increasing accuracy. In contrast therefrom, not too much is known experimentally for fermions and their gravitational interaction, apart from the celebrated Colella-Overhauser-Werner (or COW) experiment [21] using a neutron interferometer in a gravitational field.

Boundary conditions for quantum mechanics on cones and fields around cosmic strings

Abstract: We study the options for boundary conditions at the conical singularity for quantum mechanics on a two-dimensional cone with deficit angle ≦ 2π and for classical and quantum scalar fields propagating with a translationally invariant dynamics in the 1+3 dimensional spacetime around an idealized straight infinitely long, infinitesimally thin cosmic string. The key to our analysis is the observation that minus-the-Laplacian on a cone possesses a one-parameter family of selfadjoint extensions. These may be labeled by a parameterR with the dimensions of length—taking values in [0, ∞). ForR=0, the extension is positive. WhenR≠0 there is a bound state. Each of our problems has a range of possible dynamical evolutions corresponding to a range of allowedR-values. They correspond to either finite, forR=0, or logarithmically divergent, forR≠0, boundary conditions at zero radius. Non-zeroR-values are a satisfactory replacement for the (mathematically ill-defined) notion of δ-function potentials at the cone's apex. We discuss the relevance of the various idealized dynamics to quantum mechanics on a cone with a rounded-off centre and field theory around a “true” string of finite thickness. Provided one is interested in effects at sufficiently large length scales, the “true” dynamics will depend on the details of the interaction of the wave function with the cone's centre (/field with the string etc.) only through a single parameterR (its “scattering length”) and will be well-approximated by the dynamics for the corresponding idealized problem with the sameR-value. This turns out to be zero if the interaction with the centre is purely gravitational and minimally coupled, but non-zero values can be important to model nongravitational (or non-minimally coupled) interactions. Especially, we point out the relevance of non-zeroR-values to electromagnetic waves around superconducting strings. We also briefly speculate on the relevance of theR-parameter in the application of quantum mechanics on cones to 1+2 dimensional quantum gravity with massive scalars.

Gravitational stability of boson stars

Abstract: We investigate the stability of general-relativistic boson stars by classifying singularities of differential mappings and compare our results with those of perturbation theory. Depending on the particle number, the star has the following regimes of behavior: stable, metastable, pulsation, and collapse.