Showing papers on "Gravitation published in 1992"

Tensor-multi-scalar theories of gravitation

Abstract: A generic class of theories where gravity is mediated by one tensor field together with an arbitrary number of scalar fields is considered. The predictions of these theories are worked out in four different observationally relevant regimes: (i) quasi-stationary weak fields (solar system conditions); (ii) rapidly varying weak fields (gravitational wave experiments); (iii) quasi-stationary strong fields (motion of systems of compact bodies, i.e. neutron stars or black holes); and (iv) the mixing of strong and radiative field effects in the gravitational radiation of N-compact-body systems. Moreover, the authors derive several significant relations between the theoretical quantities entering these predictions. They show how strong-field-gravity effects in the motion and gravitational radiation of N-compact-body systems can be parametrized by a set of theory parameters that generalize the usual post-Newtonian parameters ( gamma , beta ,. . .) introduced in the context of quasi-stationary weak gravitational fields. These new parameters ( beta 2, beta ', beta 3, beta ",. . .) provide a chart for the yet essentially unexplored domain of strong-gravitational-field effects, and thereby suggest new directions for testing relativistic gravity. This is illustrated by studying in detail a specific two-parameter tensor-bi-scalar theory T( beta ', beta ") which has the same post-Newtonian limit as general relativity but leads to new nonEinsteinian predictions for the various observables that can be extracted from binary pulsar data.

A nonsingular universe.

Abstract: The Einstein theory of gravitation breaks down at very high curvatures. We propose a modification of the theory at Planck curvatures for which all isotropic cosmological solutions (even including matter) are nonsingular. All solutions asymptotically approach de Sitter space, a solution with limiting curvature.

Kaluza–Klein equations, Einstein’s equations, and an effective energy‐momentum tensor

Abstract: Following earlier work, it is inquired how far the 5‐D Kaluza–Klein equations without sources may be reduced to the Einstein equations with sources. It is shown by algebraic means that this can be done, provided the extra part of the 5‐D geometry is used appropriately to define an effective 4‐D energy‐momentum tensor. The latter has reasonable properties, but will require further detailed study.

Analytic approach to the perturbative expansion of nonlinear gravitational fluctuations in cosmological density and velocity fields.

Abstract: Equations of self-gravitating systems in the Universe are solved by expanding as perturbation series in Fourier space. The formulas for the higher-order terms are given for density and velocity fields. We apply the formulas to several analytically integrable models whose linear density power spectra obey a single power law, and asymptotically approach the prediction of the cold-dark-matter scenario. We explicitly give the nonlinear gravitational evolution for the fields and its dependence on the initial spectrum.

Anisotropic spheres in general relativity

Abstract: Static spheres are studied to investigate the link between the surface value of the potential (and therefore the observable redshift) and the highest occurring ratio of the trace of the pressure tensor to the local density. The transverse pressure is permitted to differ from the radial one. Both Newtonian and relativistic models are examined. Considerably larger redshift values are found when anisotropic pressures are allowed than in the isotropic case

Reinterpretation of Jordan-Brans-Dicke theory and Kaluza-Klein cosmology.

Abstract: We emphasize that it is the Pauli metric, not the Jordan metric, which describes the massless spin-two graviton in the Brans-Dicke theory. Similarly in the ``Jordan-Brans-Dicke theory'' based on Kaluza-Klein unification, only the Pauli metric can correctly describe Einstein's theory of gravitation. This necessitates a completely new reinterpretation of the ``old'' Kaluza-Klein cosmology as well as the Brans-Dicke theory. More significantly our analysis shows that the Kaluza-Klein dilaton must generate a fifth force which could violate the equivalence principle.

Gravitational wakes in Saturn's rings

Abstract: THE outer parts of Saturn's rings display a variety of local non-uniformities in their particle distributions. Azimuthal brightness variations are seen in the A-ring1,2, and may be attributable to the gravitational aggregation of particles into linear wakes that trail the rotation of the ring3–5; Voyager's stellar occultation experiments revealed large differences, on length scales as small as 150 m, in the surface density of particles6. Theoretical arguments7,8 suggest that local instabilities may occur in both the A-and B-rings, the instability criterion depending on the velocity dispersion of ring particles and the orbital velocity and mass density in the ring. These arguments, however, are derived from the purely gravitational dynamics of an idealized, infinitesimally thin ring, made of identical particles. Here I use numerical simulations, including both gravitational interactions and dissipative impacts between particles, to study realistic models of Saturn's rings. For the C-ring there is no instability, but for the B- and A-rings gravitational wakes form. In the A-ring these wakes are so strong that particles trapped in them form metre-sized aggregate particles, which themselves lead to further instability. These different behaviours are consistent with the observational evidence.

Cosmological Density Perturbations with Modified Gravity

Abstract: We determine how the usual formula for density perturbations from inflationary cosmology should be modified when the inflaton is coupled to the scalar curvature at the level of the Lagrangian. By applying a conformal transformation to a single gauge invariant quantity, we rederive a previously proposed formula for the fully coupled system in a simple and unambiguous way

The theory of scale relativity

Abstract: Basing our discussion on the relative character of all scales in nature and on the explicit dependence of physical laws on scale in quantum physics, we apply the principle of relativity to scale transformations. This principle, in combination with its breaking above the Einstein-de Broglie wavelength and time, leads to the demonstration of the existence of a universal, absolute and impassable scale in nature, which is invariant under dilatation. This lower limit to all lengths is identified with the Planck scale, which now plays for scale the same role as is played by light velocity for motion. We get new scale transformations of a Lorentzian form and generalize the de Broglie and Heisenberg relations. As a consequence the high energy length and mass scales now decouple, energy and momentum tending to infinity when resolution tends to the Planck scale, which thus plays the role of the previous zero point. This theory solves the problem of divergence of charge and mass (self-energy) in electrodynamics, implies that the four fundamental couplings (including gravitation) converge at the Planck energy, improves the agreement of GUT predictions with experimental results, and allows one to get precise estimates of the values of the fundamental coupling constants.

Simulations of Four-Dimensional Simplicial Quantum Gravity as Dynamical Triangulation

Abstract: Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: we reached about 5×104 simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. We varied the gravitational constant, and we found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). We studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths. The heavy propagator geodesic appeared to be much smoother, so that the scaling laws were found, corresponding to finite fractal dimensions: D+~2.3 in the gravity phase and D−~4.6 in the antigravity phase. Similar, but somewhat lower numbers were obtained from the heat kernel singularity. The influence of the αR2 terms in 2, 3 and 4 dimensions is discussed.

Coherent structures in the universe and the adhesion model

Abstract: An adhesion model is used to study the formation process of large-scale structures due to nonlinear gravitational growth of small initial fluctuations in the universe dominated by dark matter. The model is compared with 2D N-body simulations with initial power-law spectral indices n = -2, 0, +2, and various cutoffs. It is found that the adhesion model imitates the skeleton of the structure extremely well for the parameters of the initial spectra until the stage when the nonlinear scale reaches the correlation length R(phi) of the initial gravitational potential. The model explains the origin of large-scale coherent sructures, such as superpancakes and superfilaments, as a result of coherent motion of clumps due to large-scale inhomogeneities in the initial gravitational potential. It is found that clumps of mass identified in the N-body simulations correspond to several knots in the adhesion model, which influences the way of calculating the mass distribution function. The distribution functions of velocities and masses of clumps and areas of cells in the adhesion model satisfy self-similar scaling laws of the n = 2 model.

Causality in (2+1)-dimensional gravity

Abstract: A method is presented to characterize fully the evolution of an arbitrary set of spinless particles in (unquantized) (2+1)-dimensional gravity theory. The method produces a complete series of time ordered Cauchy surfaces, which are being triangulated. By construction, closed timelike curves never arise, even if the initial conditions contain a Gott pair. In particular the author's construction shows that the configuration proposed by Carrol et al. (1992) in which a Gott pair is formed in a closed universe, nevertheless does not admit closed timelike curves; this universe has a finite lifetime, ending in a 'big crunch'.

Einstein, Nordström, and the Early Demise of Scalar, Lorentz Covariant Theories of Gravitation

Abstract: The advent of the general theory of relativity was so entirely the work of just one person — Albert Einstein — that we cannot but wonder how long it would have taken without him for the connection between gravitation and spacetime curvature to be discovered. What would have happened if there were no Einstein? Few doubt that a theory much like special relativity would have emerged one way or another from the researchers of Lorentz, Poincare and others. But where would the problem of relativizing gravitation have led? The saga told here shows how even the most conservative approach to relativizing gravitation theory still did lead out of Minkowski spacetime to connect gravitation to a curved spacetime. Unfortunately we still cannot know if this conclusion would have been drawn rapidly without Einstein's contribution. For what led Nordstrom to the gravitational field dependence of lengths and times was a very Einsteinian insistence on just the right version of the equality of inertial and gravitational mass. Unceasingly in Nordstrom's ear was the persistent and uncompromising voice of Einstein himself demanding that Nordstrom see the most distant consequences of his own theory.

Models of Star Formation in Interacting and Merging Disk Galaxies

Abstract: We present a series of models of interactions between star-forming disk galaxies. The models employ an N-body code to calculate the gravitational dynamics, a discrete cloud model to govern the ISM dynamics, and a modified Schmidt law to describe star formation. We model both merging galaxies and more distant flyby encounters, with differing disk orientations. We find that the global star formation rates (SFRs) in merging galaxies can be increased by an order of magnitude for several hundred million years, with the vast majority of the star formation arising in the central regions of the merging galaxies

The fall of charged particles under gravity: A study of experimental problems

Abstract: There are currently proposals to test the weak equivalence principle for antimatter by studying the motion of antiprotons, negative hydrogen ions, positrons, and electrons under gravity. The motions of such charged particles are affected by residual gas, radiation, and electric and magnetic fields, as well as gravity. The electric fields are particularly sensitive to the state of the "shielding" container. This paper reviews, and extends where necessary, the physics of these extraneous influences on the motion of charged particles under gravity. The effects considered include residual gas scattering; wall potentials due to patches, stress, thermal gradients, and contamination states; and image-charge-induced dissipation.

Euler hierarchies and universal equations

Abstract: Finite Euler hierarchies of field theory Lagrangians leading to universal equations of motion for new types of string and membrane theories and for classical topological field theories are constructed. The analysis uses two main ingredients. On the one hand, there exists a generic finite Euler hierarchy for one field leading to a universal equation which generalizes the Plebanski equation of self‐dual four‐dimensional gravity. On the other hand, specific maps are introduced between field theories which provide a ‘‘triality’’ between certain classes of arbitrary field theories, classical topological field theories and generalized string and membrane theories. The universal equations, which derive from an infinity of inequivalent Lagrangians, are generalizations of certain reductions of the Plebanski and KdV equations, and could possibly define new integrable systems, thus in particular integrable membrane theories. Some classes of solutions are constructed in the general case. The general solution to some ...

Gravitational attraction of a rectangular prism with depth-dependent density

Abstract: The gravity effect produced by two and three-dimensional bodies with nonuniform density contrast has been treated by several authors. One of the first attempts in this direction made by Cordell (1973), who developed a method to compute the gravity effect due to a two-dimensional prism whose density decreases exponentially with depth. A different approach was proposed by Murthy and Rao (1979). They extended the line-integral method to obtain the gravity effect for bodies of arbitrary cross-sections, with density contrast varying linearly with depth. Chai and Hinze (1988) have derived a wavenumber-domain approach to compute the gravity effect due to a vertical prism whose density contrast varies exponentially with depth. Recently, Rao (1990) has developed a closed expression of the gravity field produced by an asymmetrical trapezoidal body whose density varies with depth following a quadratic polynomial.

The Dark Matter Problem in Light of Quantum Gravity

Abstract: We show how, by considering the cumulative effect of tiny quantum gravitational fluctuations over very large distances, it may be possible to: ($a$) reconcile nucleosynthesis bounds on the density parameter of the Universe with the predictions of inflationary cosmology, and ($b$) reproduce the inferred variation of the density parameter with distance. Our calculation can be interpreted as a computation of the contribution of quantum gravitational degrees of freedom to the (local) energy density of the Universe.

Curved-space magnetic monopoles.

Abstract: Explicit solutions of the coupled Einstein-Yang-Mills-Higgs field equations representing a 't Hooft--Polyakov--type magnetic monopole are constructed, both in and away from the Bogomolny-Prasad-Sommerfield limit. The solutions are seen to tend towards black-hole solutions as the strength of the gravitational coupling is increased, as might be expected. A careful analysis of solutions near the transition to a black hole shows that the monopole loses its non-Abelian hair as it develops a horizon. In certain cases, solutions without a horizon are seen to be unstable to gravitational collapse.