Showing papers on "Gravitational field published in 1996"

Tensor-scalar gravity and binary-pulsar experiments

Abstract: Some recently discovered nonperturbative strong-field effects in tensor-scalar theories of gravitation are interpreted as a scalar analogue of ferromagnetism: "spontaneous scalarization." This phenomenon leads to very significant deviations from general relativity in conditions involving strong gravitational fields, notably binary-pulsar experiments. Contrary to solar-system experiments, these deviations do not necessarily vanish when the weak-field scalar coupling tends to zero. We compute the scalar "form factors" measuring these deviations, and notably a parameter entering the pulsar timing observable $\ensuremath{\gamma}$ through scalar-field-induced variations of the inertia moment of the pulsar. An exploratory investigation of the confrontation between tensor-scalar theories and binary-pulsar experiments shows that nonperturbative scalar field effects are already very tightly constrained by published data on three binary-pulsar systems. We contrast the probing power of pulsar experiments with that of solar-system ones by plotting the regions they exclude in a generic two-dimensional plane of tensor-scalar theories.

Tensor-Scalar Gravity and Binary-Pulsar Experiments

Abstract: Some recently discovered nonperturbative strong-field effects in tensor-scalar theories of gravitation are interpreted as a scalar analogue of ferromagnetism: "spontaneous scalarization." This phenomenon leads to very significant deviations from general relativity in conditions involving strong gravitational fields, notably binary-pulsar experiments. Contrary to solar-system experiments, these deviations do not necessarily vanish when the weak-field scalar coupling tends to zero. We compute the scalar "form factors" measuring these deviations, and notably a parameter entering the pulsar timing observable $\ensuremath{\gamma}$ through scalar-field-induced variations of the inertia moment of the pulsar. An exploratory investigation of the confrontation between tensor-scalar theories and binary-pulsar experiments shows that nonperturbative scalar field effects are already very tightly constrained by published data on three binary-pulsar systems. We contrast the probing power of pulsar experiments with that of solar-system ones by plotting the regions they exclude in a generic two-dimensional plane of tensor-scalar theories.

Gravitational radiation from compact binary systems: Gravitational waveforms and energy loss to second post-Newtonian order.

Abstract: We derive the gravitational waveform and gravitational-wave energy flux generated by a binary star system of compact objects (neutron stars or black holes), accurate through second post-Newtonian order ($O[{(\frac{v}{c})}^{4}]=O[{(\frac{\mathrm{Gm}}{r{c}^{2}})}^{2}]$) beyond the lowest-order quadrupole approximation. We cast the Einstein equations into the form of a flat-spacetime wave equation together with a harmonic gauge condition, and solve it formally as a retarded integral over the past null cone of the chosen field point. The part of this integral that involves the matter sources and the near-zone gravitational field is evaluated in terms of multipole moments using standard techniques; the remainder of the retarded integral, extending over the radiation zone, is evaluated in a novel way. The result is a manifestly convergent and finite procedure for calculating gravitational radiation to arbitrary orders in a post-Newtonian expansion. Through second post-Newtonian order, the radiation is also shown to propagate toward the observer along true null rays of the asymptotically Schwarzschild spacetime, despite having been derived using flat-spacetime wave equations. The method cures defects that plagued previous "brute-force" slow-motion approaches to the generation of gravitational radiation, and yields results that agree perfectly with those recently obtained by a mixed post-Minkowskian post-Newtonian method. We display explicit formulas for the gravitational waveform and the energy flux for two-body systems, both in arbitrary orbits and in circular orbits. In an appendix, we extend the formalism to bodies with finite spatial extent, and derive the spin corrections to the waveform and energy loss.

Gravitational waveforms from inspiralling compact binaries to second-post-Newtonian order

Abstract: The two independent 'plus' and 'cross' polarization waveforms associated with the gravitational waves emitted by inspiralling, non-spinning, compact binaries are presented, ready for use in the data analysis of signals received by future laser interferometer gravitational-wave detectors such as LIGO and VIRGO. The computation is based on a recently derived expression of the gravitational field at the second-post-Newtonian approximation of general relativity beyond the dominant (Newtonian) quadrupolar field. The use of these theoretical waveforms to make measurements of astrophysical parameters and to test the nature of relativistic gravity is discussed.

Hyperbolic reductions for Einstein's equations

Abstract: We consider the problem of reducing initial value problems for Einstein's field equations to initial value problems for hyperbolic systems, a problem of importance for numerical as well as analytical investigations of gravitational fields. The main steps and the most important objectives in designing hyperbolic reductions are discussed. Various reductions which have already been studied in the literature or which can easily be derived from previous discussions of the field equations are pointed out and some of their specific features are indicated. We propose new reductions based on the use of the Bianchi equation for the conformal Weyl tensor. These reductions involve symmetric hyperbolic systems of propagation equations and allow a number of different gauge conditions. They use unknowns in a most economic way, supplying direct and non-redundant information about the geometry of the time slicing and the four-dimensional spacetime. Some of this information is directly related to concepts of gravitational radiation. All these reductions can be extended to include the conformal field equations. Those which are based on the ADM representation of the metric can be rewritten in flux conserving form.

On the Gauge Aspects of Gravity

Abstract: We give a short outline, in Sec.\ 2, of the historical development of the gauge idea as applied to internal ($U(1),\, SU(2),\dots$) and external ($R^4,\,SO(1,3),\dots$) symmetries and stress the fundamental importance of the corresponding conserved currents. In Sec.\ 3, experimental results with neutron interferometers in the gravitational field of the earth, as inter- preted by means of the equivalence principle, can be predicted by means of the Dirac equation in an accelerated and rotating reference frame. Using the Dirac equation in such a non-inertial frame, we describe how in a gauge- theoretical approach (see Table 1) the Einstein-Cartan theory, residing in a Riemann-Cartan spacetime encompassing torsion and curvature, arises as the simplest gravitational theory. This is set in contrast to the Einsteinian approach yielding general relativity in a Riemannian spacetime. In Secs.\ 4 and 5 we consider the conserved energy-momentum current of matter and gauge the associated translation subgroup. The Einsteinian teleparallelism theory which emerges is shown to be equivalent, for spinless matter and for electromagnetism, to general relativity. Having successfully gauged the translations, it is straightforward to gauge the four-dimensional affine group $R^4 \semidirect GL(4,R)$ or its Poincare subgroup $R^4\semidirect SO(1,3)$. We briefly report on these results in Sec.\ 6 (metric-affine geometry) and in Sec.\ 7 (metric-affine field equations (\ref{zeroth}, \ref{first}, \ref{second})). Finally, in Sec.\ 8, we collect some models, currently under discussion, which bring life into the metric-affine gauge framework developed.

Vacuum instability in external fields.

Abstract: We study particle creation from the vacuum by external electric fields, in particular, by fields, which are acting for a finite time, in the frame of QED in arbitrary space-time dimensions. In all the cases special sets of exact solutions of the Dirac equation (in and out solutions) are constructed. Using them, the characteristics of the effect are calculated. The time and dimensional analyses of the vacuum instability are presented. It is shown that the distributions of particles created by quasiconstant electric fields can be written in a form which has a thermal character and which seems to be universal, i.e., is valid for any theory with quasiconstant external fields. Its application, for example, to particle creation in an external constant gravitational field reproduces the Hawking temperature exactly. \textcopyright{} 1996 The American Physical Society.

Comparison of velocity and gravity fields: the mark III tully-fisher catalog versus the iras 1.2 jy survey

Abstract: We consider a measure of the peculiar velocity field derived from the Mark III compilation of 2900 spiral galaxies (Willick et al.), using an analysis method that is substantially free of bias (Nusser & Davis). We expand the velocity field in a set of orthogonal, smooth modes, reducing the data to a set of 56 coefficients fitted to a maximum redshift of 6000 km s–1, and maximum spherical harmonic of l = 3. The radial resolution of the modes degrades with redshift, from 800 km s–1 locally to 3000 km s–1 at 4000 km s–1 redshift. Equivalent mode coefficients can be computed for the gravity field derived from any whole-sky redshift catalog of galaxies, such as the IRAS 1.2 Jy survey (Fisher et al.). Given the coefficients of the expansions, one can compare the velocity and gravity fields on a galaxy-by-galaxy basis, or on a mode-by-mode basis. Detailed comparison shows the two independent fields to be remarkably aligned in general. There are, however, systematic discrepancies in the fields that lead to considerable coherence in the residuals between them. These residuals take the form of a dipole field in the Local Group (LG) frame that grows with distance; it is not consistent with a bulk flow residual. We perform a likelihood analysis in the mode-mode comparison to determine which value of β≡ Ω0.6/b for the IRAS gravity field is the best fit to the Mark III velocity field, considering the errors and covariance in both the velocity and gravity coefficients. We find that the most likely value lies in the range β = 0.4-0.6. However, in contrast with results we obtain using simulated galaxy catalogs, the x2 per degree of freedom for the fit is well in excess of unity, primarily because of the coherent dipole residuals at cz 3000 km s–1. Thus, despite the general alignment of the Mark III velocity and IRAS gravity fields, they do not agree in detail, precluding a firm determination of β from these data sets at present. The method is capable of measuring β to an accuracy of 10%, but without understanding these systematic discrepancies, we cannot infer a value of β from these data.

Neutrino oscillations in strong gravitational fields

Abstract: Neutrino oscillations in the presence of strong gravitational fields are studied. We look at very high energy neutrinos (\ensuremath{\sim}1 TeV) emanating from active galactic nuclei (AGN). It is observed that spin flavor resonant transitions of such neutrinos may occur in the vicinity of AGN due to gravitational effects and due to the presence of a large magnetic field (\ensuremath{\sim}1 T). A point to note is that matter effects (normal MSW transitions) become negligible in comparison to gravitational effects in our scenario.

Probing quantum gravity through exactly soluble midi‐superspaces I

Abstract: It is well‐known that the Einstein‐Rosen solutions to the 3+1‐ dimensional vacuum Einstein’s equations are in one to one correspondence with solutions of 2+1‐dimensional general relativity coupled to axi‐symmetric, zero rest mass scalar fields. We first re‐examine the quantization of this midi‐superspace paying special attention to the asymptotically flat boundary conditions and to certain functional analytic subtleties associated with regularization. We then use the resulting quantum theory to analyze several conceptual and technical issues of quantum gravity.

The helicity of the free electromagnetic field and its physical meaning

Abstract: The notion of helicity for the free electromagnetic field is analysed. The generalized helicity is introduced which is a conserved quantity coinciding with the difference of the right and left circularly polarized photons composing the electromagnetic field. It seems that it completes the list of the zilch-type invariants found by Lipkin and Ragusa. The gauge-invariant expression for the energy of the free gravitational field is obtained which strongly resembles the well-known bilinear expression for the total number of photons composing the electromagnetic field.

Solar force modeling of block IIR Global Positioning System satellites

Abstract: Scientific applications of the Global Positioning System require that the space vehicles be located with an accuracy of a few centimeters. The most important uncertainties in position estimation are the result of direct and indirect solar forces. Perhaps as early as late 1996, Block IIR space vehicles will begin to replace the existing Blocks II and IIA. We give formulas for the solar force to be expected on Block IIR and evaluate their probable accuracy based on our previous experience. These a priori formulas include indirect solar forces, including the reradiation of sunlight in the form of heat from the space vehicle's body and solar panels, but do not include radiation-induced outgassing, especially from the multilayered insulation that wraps the space vehicle body. We discuss the best way to combine these a priori models with real-time tracking data to optimize ephemeris accuracy. MONG the many unique features of the Global Positioning System (GPS), one fact is of primary importance for its use in geodesy, studies of crustal dynamics, and support of such space missions as TOPEX/Poseidon: it is the first system of navigational satellites in which errors in knowledge of the Earth's gravitational field have negligible effect, and orbit accuracy is limited almost entirely by errors in modeling the force of solar radiation on the space vehicles (SVs). These SVs are high altitude (semimajor axes = 26,560 km = 4.16 Earth radii) and relatively insensitive to the higher-order gravitational harmonics, which are well known in any case via satellites such as LAGEOS. But GPS SVs have a large cross- sectional area (about 13.6 m2 for Block II/IIA) and are accelerated about 1 x 10~7 m/s by direct solar radiation. Table 1 shows our calculation (using the Aerospace TRACE program) of perturbations on a typical GPS orbit over 12 h. After the Earth oblateness J2, the sun, and the moon, solar radiation is the most important. An a priori model calculates the solar force to be expected on the vehicle as a function of its orientation and of its cross-sectional area and optical properties. Direct solar pressure can be pictured as the net momentum imparted to the S V by photons striking and recoil- ing from its opaque surfaces. Indirect solar pressure is caused, for example, by heat absorbed and reradiated from body surfaces and by outgassing, whereby solar energy and momentum is returned to space by volatile materials on and in the SV body. Indirect forces are of two kinds: predictable, such as the effects of Earthshine and SV heat flow; and anomalous, including outgassing and the so-called 7-bias force. Because none of the indirect effects, predictable or anomalous, were included in the early computer software devel- oped for GPS, many scientific GPS analysts have bypassed the modeling problem entirely and have determined SV accelerations directly as stochastic parameters to be estimated by tracking data.1'2 To attain highest accuracy, some such real-time estimation is nec- essary. Nevertheless, good a priori models are indispensable for three reasons: 1) many applications require not just precise fitting of orbits to tracking data already taken, but orbit prediction; 2) by us- ing a standard force model, workers more readily can intercompare ephemerides, which are calculated by many different agencies from data taken all over the world using different techniques; and 3) to filter real data accurately and reliably, one should know the statistics of the parameters measured—how fast they usually change, and how fast they can change—and this requires knowledge of the physics of the problem, and therefore, good a priori modeling. Our intention

Gravitational radiation and very long baseline interferometry

Abstract: Gravitational waves affect the observed direction of light from distant sources. At telescopes, this change in direction appears as periodic variations in the apparent positions of these sources on the sky; that is, as proper motion. A wave of a given phase, traveling in a given direction, produces a characteristic pattern of proper motions over the sky. Comparison of observed proper motions with this pattern serves to test for the presence of gravitational waves. A stochastic background of waves induces apparent proper motions with specific statistical properties, and so, may also be sought. In this paper we consider the effects of a cosmological background of gravitational radiation on astrometric observations. We derive an equation for the time delay measured by two antennae observing the same source in an Einstein-de Sitter spacetime containing gravitational radiation. We also show how to obtain similar expressions for curved Friedmann-Robertson-Walker spacetimes.

Weak lensing by large-scale structure in open, flat and closed universes

Abstract: Weak lensing is the distortion (polarization) of images of distant objects, such as high-redshift galaxies, by gravitational fields in the limit where the distortion is small. Gravitational potential fluctuations arising from large-scale structure cause correlated distortions of the images of high-redshift galaxies. These distortions are observable with current large telescopes and instrumentation. In a Friedmann-Robertson-Walker (FRW) metric, I calculate the weak lensing pattern arising from large-scale structure for arbitrary no and zero cosmological 'constant A. For a given cosmological model, specified by no and a power spectrum of density fluctuations, I calculate the statistical properties of the polarization field for an arbitrary redshift source distribution in a simple closed form. It is shown that, for low redshift z of the sources, the polarization amplitude is proportional to no, while at higher redshift the polarization measures the value of n(z), where z is the characteristic source redshift. Moreover, the statistics of the polarization field are a direct measure of the power spectrum of density fluctuations.

A theory of space, time and matter

Abstract: We unify the gravitational field with its source by considering a new type of 5D manifold in which space and time are augmented by an extra dimension which induces 4D matter. The classical tests of relativity are satisfied, and for solitons we obtain new effects which can be tested astrophysically. The canonical cosmological models are in agreement with observations, and we gain new insight into the nature of the big bang. Our inference is that the world may be pure geometry in 5D.

The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons

Abstract: In many metrics of physical interest, the gravitational field can be represented as an optical medium with an effective index of refraction. We show that, in such a metric, the orbits of both massive and massless particles are governed by a variational principle which involves the index of refraction and which assumes the form of Fermat's principle or of Maupertuis's principle. From this variational principle we derive exact equations of motion of Newtonian form which govern both massless and massive particles. These equations of motion are applied to some problems of physical interest.

Seasonal Variations of the Earth's Gravitational Field: An Analysis of Atmospheric Pressure, Ocean Tidal, and Surface Water Excitation

Abstract: Monthly mean gravitational field parameters (denoted here as C(sub even)) that represent linear combinations of the primarily even degree zonal spherical harmonic coefficients of the Earth's gravitational field have been recovered using LAGEOS I data and are compared with those derived from gridded global surface pressure data of the National meteorological center (NMC) spanning 1983-1992. The effect of equilibrium ocean tides and surface water variations are also considered. Atmospheric pressure and surface water fluctuations are shown to be the dominant cause of observed annual C(sub even) variations. Closure with observations is seen at the 1sigma level when atmospheric pressure, ocean tide and surface water effects are include. Equilibrium ocean tides are shown to be the main source of excitation at the semiannual period with closure at the 1sigma level seen when both atmospheric pressure and ocean tide effects are included. The inverted barometer (IB) case is shown to give the best agreement with the observation series. The potential of the observed C(sub even) variations for monitoring mass variations in the polar regions of the Earth and the effect of the land-ocean mask in the IB calculation are discussed.

An optimal procedure for deriving marine gravity from multi-satellite altimetry

Abstract: An optimal procedure is developed for deriving gravity anomalies from sea-surface height measurements obtained by a number of different satellites, the inclinations of which may vary. We begin by recasting the problem of the conversion of the deflection of the vertical to gravity in the frequency domain. We show that a deterministic approach based on the Vening-Meinesz integral is equivalent in the frequency domain to the stochastically based method of least-squares collocation. A new method for gridding the deflection of the vertical is developed that uses the fact that satellite tracks of the same type (ascending or descending) are nearly parallel, so that values at grid points can be estimated by first performing along-track interpolations, followed by one cross-track interpolation, both using Akima's spline. This gridding method is very efficient compared with methods such as that of fitting minimum curvature surfaces, especially for dense data such as for the 168 day cycles of ERS-1. A weighted least-squares method is then employed to obtain the north and east components of deflection-of-the-vertical components using the gridded along-track components from all of the individual satellite missions. Finally, gravity anomalies are computed from the two deflection-of-the-vertical components in the frequency domain with truncated kernel functions, the use of which is related to the prior removal of a high-degree reference gravity field. This new procedure is more than 100 times faster than least-squares collocation, and yields gravity anomalies with errors that are comparable to those derived by least-squares collocation and smaller than those derived by other recent applications of spectral techniques, as judged by comparisons with ship-gravity measurements. The case of gravity computation for a single altimetric satellite is handled separately, and a method is given to estimate the noise spectra of deflection of the vertical and reduce the numerical problems caused by satellites with high inclination angles. The new procedures make possible quick, yet accurate, global updates of the marine gravity field.

I-Brane Inflow and Anomalous Couplings on D-Branes

Abstract: We show that the anomalous couplings of $D$-brane gauge and gravitational fields to Ramond-Ramond tensor potentials can be deduced by a simple anomaly inflow argument applied to intersecting $D$-branes and use this to determine the eight-form gravitational coupling.

Static and nonstatic global string.

Abstract: Exact gravitational fields due to static and nonstatic cosmic strings arising due to the breaking of a global U(1) symmetry are investigated. The results obtained are compared with that already available in the literature for the static case. One of the nonstatic solutions reduces to an essentially static form under a coordinate transformation while another does not. \textcopyright{} 1996 The American Physical Society.

Theoretical analysis of a reported weak-gravitational-shielding effect

Abstract: Under special conditions (Meissner-effect levitation in a high-frequency magnetic field and rapid rotation) a disk of high-Tc superconducting material has recently been found to produce a weak shielding of the gravitational field. We show that this phenomenon has no explanation in the standard gravity theories, except possibly in the non-perturbative Euclidean quantum theory.

Resolution of the Scripps/NOAA marine gravity field from satellite altimetry

Abstract: The July 1995 declassification of the entire Geosat GM satellite altimeter data set enabled a joint Scripps/NOAA effort to compute a new (version 7.2) marine gravity field on a 2-minute grid. This gravity field covers the world' oceans between 72°N and 72°S, and is derived from a combination of ERS-1 and Geosat GM and ERM data. An earlier NOAA Geosat-only gravity field solution was confined to the southern latitudes because the 1992 declassification was limited to GM data south of 30°S. A simple coherence analysis between accurately-navigated ship gravity profiles and comparable gravity profiles obtained from the gravity grids reveals that the Scripps/NOAA gravity field is coherent with ship gravity down to ∼≥ 23–30 km. This slight increase in resolution over the previous NOAA Geosat-only gravity field (short-wavelength resolution of ∼26–30 km) implies that the increased spatial coverage provided by the ERS-I altimeter, when combined with Geosat, improves the solution. Coherence analyses between satellite gravity and ship topography, and ship gravity and ship topography, show that even shorter wavelength gravity anomalies (∼13 km) are present in sea-surface measurements made by ship. Even so, the Scripps/NOAA marine gravity field does an excellent job of resolving most of the short-wavelength gravity anomalies covering the world’ oceans.

Astrophysical and cosmological constraints on a scale-dependent gravitational coupling

Abstract: We study the phenomenological consequences of the recently proposed idea of a running gravitational coupling on macroscopic scales. When applied to the rotation curves of galaxies, we find that their flatness requires the presence of baryonic dark matter. Bounds on the variation of the gravitational coupling from primordial nucleosynthesis and the change of the period of binary pulsars are analysed. We also study constraints on the variations of G with scale from gravitational lensing and the cosmic virial theorem, as well as briefly discuss the implications of such a scenario for structure formation.

Gravitational lensing by cosmic string loops.

Abstract: We calculate the deflection of a light ray caused by the gravitational field of a cosmic string loop in the weak field limit and reduce the problem to a single quadrature over a time slice of the loop's world sheet. We then apply this formalism to the problem of gravitational lensing by cosmic string loops. In particular, we find an analytic solution for the special case of a circular loop perpendicular to the optical axis. As examples of more complicated loops, we consider two loops with higher frequency Fourier modes. The numerical analysis illustrates the general features of loop lenses. Our estimates, using typical parameters for GUT scale loops, show that the stringy nature of loop lenses can be observed for lensing systems involving high redshift galaxies ($z\ensuremath{\sim}2$), and we suggest that gravitational lensing can confirm the existence of GUT scale strings if they are the seeds for large-scale structure formation.