Showing papers on "Gravitation published in 1998"

Rotating Stars in Relativity

Abstract: Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on equilibrium properties and on nonaxisymmetric oscillations and instabilities in f-modes and r-modes have been updated. Several new sections have been added on equilibria in modified theories of gravity, approximate universal relationships, the one-arm spiral instability, on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity including both hydrodynamic and magnetohydrodynamic studies of these objects.

The Search for Non-Newtonian Gravity

Abstract: 1 Introduction.- 2 Phenomenological Description of Non-Newtonian Gravity.- 3 Searches for Composition-Independent Effects.- 4 Searches for Composition-Dependent Effects.- 5 Gravitational Properties of Antimatter.- 6 Effects of External Forces in the Kaon System.- 7 Spin-Dependent Intermediate-Range Forces.- 8 Epilogue.- A Gravity-Gradient Couplings to Torsion Pendants.- B Luther-Towler Cavendish Experiment.- C The Earth's Gravity Field.- Author Index.

Spherically symmetric solutions of the Schrodinger-Newton equations

Abstract: As part of a programme in which quantum state reduction is understood as a gravitational phenomenon, we consider the Schrodinger-Newton equations. For a single particle, this is a coupled system consisting of the Schrodinger equation for the particle moving in its own gravitational field, where this is generated by its own probability density via the Poisson equation. Restricting to the spherically-symmetric case, we find numerical evidence for a discrete family of solutions, everywhere regular, and with normalizable wavefunctions. The solutions are labelled by the non-negative integers, the nth solution having n zeros in the wavefunction. Furthermore, these are the only globally defined solutions. Analytical support is provided for some of the features found numerically.

The running gravitational couplings

Abstract: We compute the running of the cosmological constant and Newton's constant at sub-Planckian energies, taking into account the effect of quantum fields with any spin between 0 and 2. We find that Newton's constant does not vary appreciably but the cosmological constant can change by many orders of magnitude when one goes from cosmological scales to typical elementary particle scales. In the extreme infrared, zero modes drive a positive cosmological constant to zero.

Born - Infeld - Einstein actions?

Abstract: We present some obvious physical requirements on gravitational avatars of nonlinear electrodynamics and illustrate them with explicit determinantal Born - Infeld - Einstein models. A related procedure, using compensating Weyl scalars, permits us to formulate conformally invariant versions of these systems as well.

Test of general relativity and measurement of the lense-thirring effect with two earth satellites

Abstract: The Lense-Thirring effect, a tiny perturbation of the orbit of a particle caused by the spin of the attracting body, was accurately measured with the use of the data of two laser-ranged satellites, LAGEOS and LAGEOS II, and the Earth gravitational model EGM-96. The parameter μ, which measures the strength of the Lense-Thirring effect, was found to be 1.1 ± 0.2; general relativity predicts μ ≡ 1. This result represents an accurate test and measurement of one of the fundamental predictions of general relativity, that the spin of a body changes the geometry of the universe by generating space-time curvature.

Gravitational wave versus binary - pulsar tests of strong field gravity

Abstract: Binary systems comprising at least one neutron star contain strong gravitational field regions and thereby provide a testing ground for strong-field gravity. Two types of data can be used to test the law of gravity in compact binaries: binary pulsar observations, or forthcoming gravitational-wave observations of inspiralling binaries. We compare the probing power of these two types of observations within a generic two-parameter family of tensor-scalar gravitational theories. Our analysis generalizes previous work (by us) on binary-pulsar tests by using a sample of realistic equations of state for nuclear matter (instead of a polytrope), and goes beyond a previous study (by C.M. Will) of gravitational-wave tests by considering more general tensor-scalar theories than the one-parameter Jordan-Fierz-Brans-Dicke one. Finite-size effects in tensor-scalar gravity are also discussed.

Conformal transformations in classical gravitational theories and in cosmology

Abstract: In recent years, the use of conformal transformation techniques has become widespread in the literature on gravitational theories alternative to general relativity, on cosmology, and on nonminimally coupled scalar fields. Typically, the transformation to the Einstein frame is generated by a fundamental scalar field already present in the theory. In this context, the problem of which conformal frame is the physical one has to be dealt with and, in the general case, it has been clarified only recently; the formulation of a theory in the ``new'' conformal frame leads to departures from canonical Einstein gravity. In this article, we review the literature on conformal transformations in classical gravitational theories and in cosmology, seen both as purely mathematical tools and as maps with physically relevant aspects. It appears particularly urgent to refer the analysis of experimental tests of Brans-Dicke and scalar-tensor theories of gravity, as well as the predictions of cosmological inflationary scenarios, to the physical conformal frame, in order to have a meaningful comparison with the observations.

The Time evolution of bias

Abstract: We study the evolution of the bias factor b and the mass-galaxy correlation coefficient r in a simple analytic model for galaxy formation and the gravitational growth of clustering. The model shows that b and r can be strongly time dependent but tend to approach unity even if galaxy formation never ends as the gravitational growth of clustering debiases the older galaxies. The presence of random fluctuations in the sites of galaxy formation relative to the mass distribution can cause large and rapidly falling bias values at high redshift.

Classical monopoles: Newton, NUT space, gravomagnetic lensing, and atomic spectra

Abstract: This article reviews the dynamics and observational signatures of particles interacting with monopoles, beginning with a scholium in Newton'sPrincipia. The orbits of particles in the field of a gravomagnetic monopole, the gravitational analog of a magnetic monopole, lie on cones; when the cones are slit open and flattened, the orbits are the ellipses and hyperbolas that one would have obtained without the gravomagnetic monopole. The more complex problem of a charged, spinning sphere in the field of a magnetic monopole is then discussed. The quantum-mechanical generalization of this latter problem is that of monopolar hydrogen. Previous work on monopolar hydrogen is reviewed and details of the predicted spectrum are given. Protons around uncharged monopoles have a bound continuum. Around charged ones, electrons have levels and decaying resonances, so magnetic monopoles can grow in mass by swallowing both electrons and protons. In general relativity, the spacetime produced by a gravomagnetic monopole is NUT space, named for Newman, Tamborino, and Unti (1963). This space has a nonspherical metric, even though a mass with a gravomagnetic monopole is spherically symmetric. All geodesics in NUT space lie on cones, and this result is used to discuss the gravitational lensing by bodies with gravomagnetic monopoles.

On the Formation and Evolution of Disk Galaxies: Cosmological Initial Conditions and the Gravitational Collapse

Abstract: We use a semianalytical approach and the standard σ8 = 1 cold dark matter (SCDM) cosmological model to study the gravitational collapse and virialization, the structure, and the global and statistical properties of isolated dark matter galactic halos that emerge from primordial Gaussian fluctuations First, from the statistical properties of the primordial density fluctuation field, the possible mass aggregation histories (MAHs) are generated Second, these histories are used as the initial conditions of the gravitational collapse To calculate the structure of the virialized systems, we have generalized the secondary infall model to allow arbitrary MAHs and internal thermal motions The average halo density profiles we obtained agree with the profile derived as a fitting formula to results of N-body cosmological simulations by Navarro, Frenk, & White The comparison of the density profiles with the observational data is discussed, and some possible solutions to the disagreement found in the inner regions are proposed The results of our approach, after considering the gravitational dragging of the baryon matter that forms a central disk in centrifugal equilibrium, show that the empirical Tully-Fisher (TF) relation and its scatter can be explained through the initial cosmological conditions, at least for the isolated systems The σ8 = 1 SCDM model produces galaxies with high velocities when compared with observations, but when the SCDM power spectrum is normalized to σ8 = 057, an excellent agreement with the observable TF relation is found, suggesting that this relation is the natural extension to galactic scales of the observed galaxy distribution power spectrum The theoretical TF scatter is close to the measured one The slope of the TF relation is practically invariant with respect to the spin parameter λ

Testing the hypothesis of modified dynamics with low surface brightness galaxies and other evidence

Abstract: The rotation curves of low surface brightness galaxies provide a unique data set with which to test alternative theories of gravitation over a large dynamic range in size, mass, surface density, and acceleration. Many clearly fail, including any in which the mass discrepancy appears at a particular length scale. One hypothesis, Modified Newtonian Dynamics (MOND), is consistent with the data. Indeed, it accurately predicts the observed behavior. We find no evidence on any scale that clearly contradicts MOND and much that supports it.

Conformal transformations in classical gravitational theories and in cosmology

Abstract: In recent years, the use of conformal transformation techniques has become widespread in the literature on gravitational theories alternative to general relativity, on cosmology, and on nonminimally coupled scalar fields. Typically, the transformation to the Einstein frame is generated by a fundamental scalar field already present in the theory. In this context, the problem of which conformal frame is the physical one has to be dealt with and, in the general case, it has been clarified only recently; the formulation of a theory in the ``new'' conformal frame leads to departures from canonical Einstein gravity. In this article, we review the literature on conformal transformations in classical gravitational theories and in cosmology, seen both as purely mathematical tools and as maps with physically relevant aspects. It appears particularly urgent to refer the analysis of experimental tests of Brans-Dicke and scalar-tensor theories of gravity, as well as the predictions of cosmological inflationary scenarios, to the physical conformal frame, in order to have a meaningful comparison with the observations.

Relativistic Diskoseismology

Abstract: We will summarize results of calculations of the modes of oscillation trapped within the inner region of accretion disks by the strong-field gravitational properties of a black hole (or a compact, weakly-magnetized neutron star) Their driving and damping will also be addressed The focus will be on the most observable class: the analogue of internal gravity modes in stars Their frequencies which corrrespond to the lowest mode numbers depend almost entirely upon only the mass and angular momentum of the black hole Such a feature may have been detected in the X-ray power spectra of two galactic `microquasars', allowing the angular momentum of the black hole to be determined in one case

The Hierarchy Problem and New Dimensions at a Millimeter

Abstract: We propose a new framework for solving the hierarchy problem which does not rely on either supersymmetry or technicolor. In this framework, the gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature. The observed weakness of gravity on distances $\gsim$ 1 mm is due to the existence of $n \geq 2$ new compact spatial dimensions large compared to the weak scale. The Planck scale $M_{Pl} \sim G_N^{-1/2}$ is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. While gravitons can freely propagate in the new dimensions, at sub-weak energies the Standard Model (SM) fields must be localized to a 4-dimensional manifold of weak scale "thickness" in the extra dimensions. This picture leads to a number of striking signals for accelerator and laboratory experiments. For the case of $n=2$ new dimensions, planned sub-millimeter measurements of gravity may observe the transition from $1/r^2 \to 1/r^4$ Newtonian gravitation. For any number of new dimensions, the LHC and NLC could observe strong quantum gravitational interactions. Furthermore, SM particles can be kicked off our 4 dimensional manifold into the new dimensions, carrying away energy, and leading to an abrupt decrease in events with high transverse momentum $p_T \gsim$ TeV. For certain compact manifolds, such particles will keep circling in the extra dimensions, periodically returning, colliding with and depositing energy to our four dimensional vacuum with frequencies of $ \sim 10^{12}$ Hz or larger. As a concrete illustration, we construct a model with SM fields localised on the 4-dimensional throat of a vortex in 6 dimensions, with a Pati-Salam gauge symmetry $SU(4) \times SU(2) \times SU(2)$ in the bulk.

Out Of This World Supersymmetry Breaking

Abstract: We show that in a general hidden sector model, supersymmetry breaking necessarily generates at one-loop a scalar and gaugino mass as a consequence of the super-Weyl anomaly. We study a scenario in which this contribution dominates. We consider the Standard Model particles to be localized on a (3+1)-dimensional subspace or ``3-brane'' of a higher dimensional spacetime, while supersymmetry breaking occurs off the 3-brane, either in the bulk or on another 3-brane. At least one extra dimension is assumed to be compactified roughly one to two orders of magnitude below the four-dimensional Planck scale. This framework is phenomenologically very attractive; it introduces new possibilities for solving the supersymmetric flavor problem, the gaugino mass problem, the supersymmetric CP problem, and the mu-problem. Furthermore, the compactification scale can be consistent with a unification of gauge and gravitational couplings. We demonstrate these claims in a four-dimensional effective theory below the compactification scale that incorporates the relevant features of the underlying higher dimensional theory and the contribution of the super-Weyl anomaly. Naturalness constraints follow not only from symmetries but also from the higher dimensional origins of the theory. We also introduce additional bulk contributions to the MSSM soft masses. This scenario is very predictive: the gaugino masses, squark masses, and $A$ terms are given in terms of MSSM renormalization group functions.

Moon-Earth-Sun: The oldest three-body problem

Abstract: The daily motion of the Moon through the sky has many unusual features that a careful observer can discover without the help of instruments. The three different frequencies for the three degrees of freedom have been known very accurately for 3000 years, and the geometric explanation of the Greek astronomers was basically correct. Whereas Kepler's laws are sufficient for describing the motion of the planets around the Sun, even the most obvious facts about the lunar motion cannot be understood without the gravitational attraction of both the Earth and the Sun. Newton discussed this problem at great length, and with mixed success; it was the only testing ground for his Universal Gravitation. This background for today's many-body theory is discussed in some detail because all the guiding principles for our understanding can be traced to the earliest developments of astronomy. They are the oldest results of scientific inquiry, and they were the first ones to be confirmed by the great physicist-mathematicians of the 18th century. By a variety of methods, Laplace was able to claim complete agreement of celestial mechanics with the astronomical observations. Lagrange initiated a new trend wherein the mathematical problems of mechanics could all be solved by the same uniform process; canonical transformations eventually won the field. They were used for the first time on a large scale by Delaunay to find the ultimate solution of the lunar problem by perturbing the solution of the two-body Earth-Moon problem. Hill then treated the lunar trajectory as a displacement from a periodic orbit that is an exact solution of a restricted three-body problem. Newton's difficultly in explaining the motion of the lunar perigee was finally resolved, and the Moon's orbit was computed by a new method that became the universal standard until after WW II. Poincar\'e opened the 20th century with his analysis of trajectories in phase space, his insistence on investigating periodic orbits even in ergodic systems, and his critique of perturbation theory, particularly in the case of the Moon's motion. Space exploration, astrophysics, and the landing of the astronauts on the Moon led to a new flowering of celestial mechanics. Lunar theory now has to confront many new data beyond the simple three-body problem in order to improve its accuracy below the precision of 1 arcsecond; the computer dominates all the theoretical advances. This review is intended as a case study of the many stages that characterize the slow development of a problem in physics from simple observations through many forms of explanation to a high-precision fit with the data.

Quantum theory of gravitation

Abstract: It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry The algebraic method is extended to obtain solutions of Einstein’s gravitational field equations for empty space, with a cosmological term General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein"s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) ⊗ SO(4; 2) There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation

Fast Calculation of a Family of Elliptical Gravitational Lens Models

Abstract: Because of their simplicity, axisymmetric mass distributions are often used to model gravitational lenses. Since galaxies are usually observed to have elliptical light distributions, mass distributions with elliptical density contours offer more general and realistic lens models. They are difficult to use, however, since previous studies have shown that the deflection angle (and magnification) in this case can only be obtained by rather expensive numerical integrations. We present a family of lens models for which the deflection can be calculated to high relative accuracy (10-5) with a greatly reduced numerical effort, for small and large ellipticity alike. This makes it easier to use these distributions for modeling individual lenses as well as for applications requiring larger computing times, such as statistical lensing studies. A program implementing this method can be obtained from the author.

Why Is the Cosmic Microwave Background Fluctuation Level 10?5?

Abstract: We explore the qualitative changes that would occur if the amplitude Q ~ 10-5 of cosmological density fluctuations were different. If Q 10-6, the cosmological objects that form would have such low virial temperatures that they may be unable to cool and form stars, and they would be so loosely bound that even if they could produce a supernova explosion they might be unable to retain the heavy elements necessary for planetary life. If Q 10-4, dense supermassive galaxies would form, and biological evolution could be marred by short disruption timescales for planetary orbits. If Q were still larger, most bound systems would collapse directly to supermassive black holes. These constraints on Q can be expressed in terms of fundamental constants alone and depend only on the electromagnetic and gravitational coupling constants, the electron-proton mass ratio, and the matter-to-photon ratio. We discuss the implications for inflation and defect models and note that the recent anthropic upper bounds on the cosmological constant Λ would be invalid if both Q and Λ could vary and there were no anthropic constraints on Q. The same applies to anthropic bounds on the curvature parameter Ω.

Neutron stars in scalar-tensor theories of gravity and catastrophe theory

Abstract: We investigate neutron stars in scalar-tensor theories. We examine their secular stability against spherically symmetric perturbations by use of a turning point method. For some choices of the coupling function contained in the theories, the number of the stable equilibrium solutions changes and the realized equilibrium solution may change discontinuously as the asymptotic value of the scalar field or total baryon number is changed continuously. The behavior of the stable equilibrium solutions is explained by fold and cusp catastrophes. Whether or not the cusp catastrophe appears depends on the choice of the coupling function. These types of catastrophes are structurally stable. Recently discovered spontaneous scalarization, which is a nonperturbative strong-field phenomenon due to the presence of the gravitational scalar field, is well described in terms of the cusp catastrophe.

Spacetime Foam as a Quantum Thermal Bath

Abstract: An effective model for the spacetime foam is constructed in terms of nonlocal interactions in a classical background. In the weak coupling approximation, the evolution of the low-energy density matrix is determined by a master equation that predicts loss of quantum coherence. Moreover, spacetime foam can be described by a quantum thermal field that, apart from inducing loss of coherence, gives rise to effects such as gravitational Lamb and Stark shifts as well as quantum damping in the evolution of the low-energy observables.

Topological gravity as large N topological gauge theory

Abstract: We consider topological closed string theories on Calabi-Yau manifolds which compute superpotential terms in the corresponding compactified type II effective action. In particular, near certain singularities we compare the partition function of this topological theory (the Kodaira-Spencer theory) to $SU(\infty)$ Chern-Simons theory on the vanishing 3-cycle. We find agreement between these theories, which we check explicitly for the case of shrinking $S^3$ and Lens spaces, at the perturbative level. Moreover, the gauge theory has non-perturbative contributions which have a natural interpretation in the Type IIB picture. We provide a heuristic explanation for this agreement as well as suggest further equivalences in other topological gravity/gauge systems.

Normalizing the Temperature Function of Clusters of Galaxies

Abstract: We reexamine the constraints that can be robustly obtained from the observed temperature function of X-ray studies of cluster of galaxies. The cluster mass function has been thoroughly and analytically studied in simulations, but a direct simulation of the temperature function is presented here for the first time. Adaptive hydrodynamic simulations using the cosmological Moving Mesh Hydro code are used to calibrate the temperature function for different popular cosmologies. Applying the new normalizations to the present-day cluster abundances, we find σ8=0.53±0.05Ω−0.450 for a hyperbolic universe and σ8 = 0.53±0.05Ω−0.530 for a spatially flat universe with a cosmological constant. The simulations followed the gravitational shock heating of the gas and dark matter and used a crude model for energy injection by supernova heating. The error bars are dominated by uncertainties in the heating/cooling models. We present fitting formulae for the mass-temperature conversions and cluster abundances based on these simulations.

1E0657-56: A Contender for the Hottest Known Cluster of Galaxies

Abstract: We identify the extended Einstein IPC X-ray source, 1E0657-56, with a previously unknown cluster of galaxies at a redshift of $z=0.296$. Optical CCD images show the presence of a gravitational arc in this cluster and galaxy spectra yield a cluster velocity dispersion of $1213^{+352}_{-191}$ km s$^{-1}$. X-ray data obtained with the ROSAT HRI and ASCA indicate that 1E0657-56 is a highly luminous cluster in which a merger of subclusters may be occurring. The temperature of the hot gas in 1E0657-56 is $\rm{kT}=17.4 \pm 2.5 keV$, which makes it an unusually hot cluster, with important cosmological implications.

Effective Nonlocal Euclidean Gravity

Abstract: A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newtonian constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value Ω < 1 for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.

Repulsive gravity in the very early universe

Abstract: I present two examples in which the curvature singularity of a radiation-dominated Universe is regularized by (a) the repulsive effects of spin interactions, and (b) the repulsive effects arising from a breaking of the local gravitational gauge symmetry. In both cases the collapse of an initial, asymptotically flat state is stopped, and the Universe bounces towards a state of decelerated expansion. The emerging picture is typical of the pre-big bang scenario, with the main difference that the string cosmology dilaton is replaced by a classical radiation fluid, and the solutions are not duality-invariant.

Equations of motion of a spinning relativistic particle in external fields

Abstract: We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields to first order in the external field but to arbitrary order in the spin. The influence of the spin on the particle trajectory is properly accounted for by describing the spin noncovariantly. Specific calculations are performed through second order in the spin. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a particular spin effect in general relativity. We show that for a Kerr black hole the gravimagnetic ratio, i.e., the coefficient of the GM, equals unity (just as the gyromagnetic ratio equals 2 for a charged Kerr hole). The equations of motion obtained for a spinning relativistic particle in an external gravitational field differ substantially from the Papapetrou equations.