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The University of Virginia, Theoretical High Energy Physics (Final Technical Report)
We summarize research performed in the final reporting period of grant DE-SC0007984 for University of Virginia, Theoretical High Energy Physics. Progress was made on studying quantum mechanical effects in the showering of high energy particles inside a quark-gluon plasma, on the effects of extra dimensions on gravitational waves, and on expanding the use of what is known as the "worldline" formalism in quantum field theory.
Massive stars in quasi-static equilibrium.
Quasi-static equilibrium in massive stars during gravitational contraction including discussion of general relativistic and classical hydrodynamic results
Planetary Interior Modeling and Tectonic Implications
A technique is described for estimating spectral admittance functions using Pioneer Venus gravity and topography data. These admittance functions provide a convenient means to carry out systematic geophysical studies over much of the surface of Venus with a variety of interior density models. The admittance functions are calculated in the observation space of line-of-sight (LOS) gravity. Both closed and open system petrological models are considered for the Tharsis region of Mars. An analytic theory for isostatic compensation on one-plate planet is applied, including membrane stresses in the lithosphere, self gravitation, and rotational ellipticity. Crucial to this stress modeling and also to the petrological modeling is the observation that the earliest fracturing seen in the Tharsis region is associated with isostatic stresses. The radial fractures that extend far from Tharsis are associated with an additional and/or a completely different mechanism.
Angular momentum growth in protogalaxies
An analysis by Doroshkevich (1970) which shows that the angular momentum of galaxies grew to first order (in proportion to t) during the linear phases of protogalactic evolution is expanded. This result is confirmed in N-body simulations of the formation of structure. The well-known study of Peebles (1969) found growth at second order only (in proportion to t to the 5/3-power) because its analysis was restricted to spherical regions. In such regions growth occurs purely as a result of convective effects on the bounding surface; the material initially within a spherical volume gains no angular momentum in second-order perturbation theory. These considerations do not affect estimates of the total angular momentum acquired by a galaxy in the gravitational instability picture.
Further explorations of cosmogonic shadow effects in the Saturnian rings
The mass distribution in the Saturnian ring system is compared with predictions from the cosmogonic theory of Alfven and Arrhenius (1975) in which matter in the rings was once a magnetized plasma, with gravitation balanced by centrifugal force and by the magnetic field. As the plasma is neutralized, the magnetic force disappears and the matter can be shown to fall in to a distance 2/3 of the original. This supports the cosmogonic shadow effect, also demonstrated for the astroidal belt and in the large scale structure of the Saturnian ring system. The relevance of the comogonic shadow effect for parts of the finer structures of the Saturnian ring system is investigated. It is shown that many structures of the present ring system can be understood as shadows and antishadows of cosmogonic origin. These appear in the form of double rings centered around a position a factor 0.64 (slightly 2/3) closer to Saturn than the causing feature.
False vacuum decay in Jordan-Brans-Dicke cosmologies
The bubble nucleation rate in a first-order phase transition taking place in a background Jordan-Brans-Dicke cosmology is examined. The leading order terms in the nucleation rate when the Jordan-Brans-Dicke field is large (i.e., late times) are computed by means of a Weyl rescaling of the fields in the theory. It is found that despite the fact that the Jordan-Brans-Dicke field (hence the effective gravitational constant) has a time dependence in the false vacuum at late times the nucleation rate is time independent.
Galactic oscillator symmetry
Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.
Modeling of micro thrusters for gravity probe B
The concept of testing Einstein's general theory of relativity by means of orbiting gyroscopes was first proposed in 1959, which lead to the development of the Gravity Probe B experiment. Einstein's theory concerns the predictions of the relativistic precession of a gyroscope in orbit around earth. According to his theory, there will be two precessions due to the warping of space-time by the earth's gravitational field: the geodetic precession in the plane of the orbit, and the frame-dragging effect, in the direction of earth rotation. For a polar orbit, these components are orthogonal. In order to simplify the measurement of the precessions, Gravity Probe B (GP-B) will be placed in a circular polar orbit at 650 km, for which the predicted precessions will be 6.6 arcsec/year (geodetic) and 42 milli-arcsec/year (frame-dragging). As the gyroscope precesses, the orientation of its spin-axis will be measured with respect to the line-of-sight to Rigel, a star whose proper motion is known to be within the required accuracy. The line-of-sight to Rigel will be established using a telescope, and the orientation of the gyroscope spin axis will be measured using very sensitive SQUID (Superconducting Quantum Interference Device) magnetometers. The four gyroscopes will be coated with niobium. Below 2K, the niobium becomes superconducting and a dipole field will be generated which is precisely aligned with the gyroscope spin-axis. The change in orientation of these fields, as well as the spin-axis, is sensed by the SQUID magnetometers. In order to attain the superconducting temperatures for the gyroscopes and the SQUID's, the experiment package will be housed in a dewar filled with liquid helium. The helium flow through a GP-B micro thruster and into a vacuum is investigated using the Direct Simulation Monte Carlo method.
Testing Einstein's Gravity on Large Scales
A little over a decade has passed since two teams studying high redshift Type Ia supernovae announced the discovery that the expansion of the universe was accelerating. After all this time, we?re still not sure how cosmic acceleration fits into the theory that tells us about the large-scale universe: General Relativity (GR). As part of our search for answers, we have been forced to question GR itself. But how will we test our ideas? We are fortunate enough to be entering the era of precision cosmology, where the standard model of gravity can be subjected to more rigorous testing. Various techniques will be employed over the next decade or two in the effort to better understand cosmic acceleration and the theory behind it. In this talk, I will describe cosmic acceleration, current proposals to explain it, and weak gravitational lensing, an observational effect that allows us to do the necessary precision cosmology.
Contribution to the theory of the perturbed Kepler motion of a material point in the presence of a small tangential force
Equations of motion for geopotential determination of central gravitational field of earth influenced by tangential force
Spin and gravitation
The fundamental variational principle for a perfect fluid in general relativity is extended so that it applies to the metric-torsion Einstein-Cartan theory. Field equations for a perfect fluid in the Einstein-Cartan theory are deduced. In addition, the equations of motion for a fluid with intrinsic spin in general relativity are deduced from a special relativistic variational principle. The theory is a direct extension of the theory of nonspinning fluids in special relativity.
Detectability of QCD phase transitions in binary neutron star mergers: Bayesian inference with the next generation gravitational wave detectors
We study the detectability of postmerger QCD phase transitions in neutron star binaries with next-generation gravitational-wave detectors Cosmic Explorer and Einstein Telescope. We perform numerical relativity simulations of neutron star mergers with equations of state that include a quark deconfinement phase transition through either a Gibbs or Maxwell construction. These are followed by Bayesian parameter estimation of the associated gravitational-wave signals using the nrpmw waveform model, with priors inferred from the analysis of the inspiral signal. We assess the ability of the model to measure the postmerger peak frequency $f$$^{peak}_{2}$ and identify aspects that should be improved in the model. We show that, even at postmerger signal to noise ratios as low as 10, the model can distinguish (at the 90% level) $f$$^{peak}_{2}$ between binaries with and without a phase transition in most cases. Phase-transition induced deviations in the $f$$^{peak}_{2}$ from the predictions of equation-of-state insensitive relations can also be detected if they exceed 1.6σ. Our results suggest that next-generation gravitational wave detectors can measure phase transition effects in binary neutron star mergers. Furthermore, unless the phase transition is “strong,” disentangling it from other hadronic physics uncertainties will require significant theory improvements.
Tests of general relativity using Starprobe radio metric tracking data
The potential of a proposed spacecraft mission, called Starprobe, for testing general relativity and providing information on the interior structure and dynamics of the sun is investigated. Parametric, gravitational perturbation terms are derived which represent relativistic effects and effects due to spatial and temporal variations in the solar potential at a given radial distance. A covariance analysis based on Kalman filtering theory predicts the accuracies with which the free parameters in the perturbation terms can be estimated with radio metric tracking data through the process of trajectory reconstruction. It is concluded that Starprobe can contribute significant information on both the nature of gravitation and the structure and dynamics of the solar interior.
Static response and Love numbers of Schwarzschild black holes
We derive the quadratic action for the physical degrees of freedom of massless spin-0, spin-1, and spin-2 perturbations on a Schwarzschild-(A)dS background in arbitrary dimensions. Here, we then use these results to compute the static response of asymptotically flat Schwarzschild black holes to external fields. Our analysis reproduces known facts about black hole Love numbers — in particular that they vanish for all types of perturbation in four spacetime dimensions — but also leads to new results. For instance, we find that neutral Schwarzschild black holes polarize in the presence of an electromagnetic background in any number of spacetime dimensions except four. Moreover, we calculate for the first time black hole Love numbers for vector-type gravitational perturbations in higher dimensions and find that they generically do not vanish. Along the way, we shed some light on an apparent discrepancy between previous results in the literature, and clarify some aspects of the matching between perturbative calculations of static response on a Schwarzschild background and the point-particle effective theory.
OORT-Cloud and Kuiper-Belt Comets
This paper follows the broadly accepted theory that Oort-Cloud Comets originated in the Solar Nebula in the general region where the major planets, Jupiter and Saturn, were formed while the Kuiper-Belt Comets originated farther out where the temperatures were lower. The Oort-Cloud Comets are identified orbitally by long periods and random inclinations and, including the Halley-type comets, comets with a Tisserand Criterion less than 2.0. Kuiper-Belt comets are identified by short periods, usually much less than 200 years, and small inclinations to the ecliptic. Here two criteria for comet activity are found to separate the two classes of comets. These quantities NG1 and NG2, were intended to measure theoretical nongravitaional effects on comet orbits. They are only, mildly successful in correlations with observed cases of measured non-gravitational forces. But, in fact, their variations with perihelion distance separate the two classes of comets. The results are consistent with the theory that the activity or intrinsic brightness of Oort-Cloud Comets fall off faster with increasing perihelion distance that does the intrinsic brightness of short-period Kuiper-Belt Comets.
Ring Formation in Protoplanetary Disks Driven by an Eccentric Instability
We find that, under certain conditions, protoplanetary disks may spontaneously generate multiple, concentric gas rings without an embedded planet through an eccentric cooling instability. Using both linear theory and nonlinear hydrodynamics simulations, we show that a variety of background states may trap a slowly processing, one-armed spiral mode that becomes unstable when a gravitationally stable disk rapidly cools. The angular momentum required to excite this spiral comes at the expense of nonuniform mass transport that generically results in multiple rings. For example, one long-term hydrodynamics simulation exhibits four long-lived, axisymmetric gas rings. We verify the instability evolution and ring-formation mechanism from first principles with our linear theory, which shows remarkable agreement with the simulation results. Dust trapped in these rings may produce observable features consistent with observed disks. Additionally, direct detection of the eccentric gas motions may be possible when the instability saturates, and any residual eccentricity left over in the rings at later times may also provide direct observational evidence of this mechanism.
A gravitationally induced
Gravitationally induced /Machian/ magnetic field by rotating mass-shell with centrally located stationary charged sphere, using linearized relativity theory