Arkady Kheyfets

Spin dynamics of the LAGEOS satellite in support of a measurement of the Earth's gravitomagnetism.

LAGEOS is an accurately tracked, dense spherical satellite covered with 426 retroreflectors. Ciufolini has suggested the launch of an additional satellite (LAGEOS-3) into an orbit supplementary to that of the 1976-launched LAGEOS-1. In addition to providing a more accurate real-time measurement of the Earths length of day and polar wobble, this paired-satellite experiment would provide the first direct measurement of the general relativistic frame-dragging effect. Of the five dominant error sources in this experiment, the largest one involves surface forces on the satellite, and their consequent impact on the orbital nodal precession. The surface forces are a function of the spin dynamics of the satellite. Consequently, we undertake here a theoretical effort to model the spin dynamics of LAGEOS. In this paper we derive, and solve numerically, a set of Euler equations that evolve the angular momentum vector for a slightly oblate spheroid of brass orbiting an Earth-like mass, idealized as being a perfect sphere and having a perfect polar-oriented dipole magnetic field. We have identified three phases of the rotational dynamics---a fast spin phase, a spin-orbit resonance phase, and an asymptotic (tidally locked) phase. From our numerical runs we give analytic expressions for this tidally locked phase.

Off-Axis Neutrino Scattering in Gamma-Ray Burst Central Engines

The search for an understanding of an energy source great enough to explain the gamma-ray burst (GRB) phenomenon has attracted much attention from the astrophysical community since its discovery. In this paper we extend the work of Asano and Fukuyama, and Salmonson and Wilson and analyze the off-axis contributions to the energy-momentum deposition rate (MDR) from the ν- collisions above a rotating black hole/thin accretion disk system. Our calculations are performed by imaging the accretion disk at a specified observer using the full geodesic equations and calculating the cumulative MDR from the scattering of all pairs of neutrinos and antineutrinos arriving at the observer. Our results shed light on the beaming efficiency of GRB models of this kind. Although we confirm Asano and Fukuyamas conjecture as to the constancy of the beaming for small angles away from the axis, we find that the dominant contribution to the MDR comes from near the surface of the disk with a tilt of approximately π/4 in the direction of the disks rotation. We find that the MDR at large radii is directed outward in a conic section centered around the symmetry axis and is larger by a factor of 10-20 than the on-axis values. By including this off-axis disk source, we find a linear dependence of the MDR on the black hole angular momentum.

Schild's Ladder Parallel Transport Procedure for an Arbitrary Connection

We analyze the Schilds ladder parallel transport procedure for an arbitraryconnection. We demonstrate that the procedure, while it can be performed forany connection, in fact is only capable of detecting the symmetric part of thisconnection. In geometries with a symmetric connection it fulfills its goal toexpress connection and parallel transport of any vector in terms of geodesics ofsuch geometries.

A Kirchhoff-like conservation law in Regge calculus

Simplicial lattices provide an elegant framework for discrete spacetimes. The inherent orthogonality between a simplicial lattice and its circumcentric dual yields an austere representation of spacetime which provides a conceptually simple form of Einsteins geometric theory of gravitation. A sufficient understanding of simplicial spacetimes has been demonstrated in the literature for spacetimes devoid of all non-gravitational sources. However, this understanding has not been adequately extended to non-vacuum spacetime models. Consequently, a deep understanding of the diffeomorphic structure of the discrete theory is lacking. Conservation laws and symmetry properties are attractive starting points for coupling matter with the lattice. We present a simplicial form of the contracted Bianchi identity which is based on the E Cartan moment of rotation operator. This identity manifests itself in the conceptually simple form of a Kirchhoff-like conservation law. This conservation law enables one to extend Regge calculus to non-vacuum spacetimes and provides a deeper understanding of the simplicial diffeomorphism group.

Quantum geometrodynamics: Quantum-driven many-fingered time.

The classical theory of gravity predicts its own demise---singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the constraints as expectation-value equations over the true dynamical degrees of freedom of the gravitational field---a representation of the underlying anisotropy of space. This self-consistent approach leads to qualitatively different predictions than the Dirac and the ADM quantizations, and, in addition, our theory avoids the interpretational conundrums associated with the problem of time in quantum gravity. We briefly describe the structure of our functional equations, and apply our quantization technique to two examples so as to illustrate the basic ideas of our approach.

The boundary of a boundary principle in field theories and the issue of austerity of the laws of physics

The boundary of a boundary principle has been suggested by J. A. Wheeler as a realization of the austerity idea in field theories. This principle is described in three basic field theories—electrodynamics, Yang–Mills theory, and general relativity. It is demonstrated that it supplies a unified geometric interpretation of the source current in each of the three theories in terms of a generalized E. Cartan moment of rotation. The extent to which the boundary of a boundary principle represents the austerity principle is discussed. It is concluded that it works in a way analogous to thermodynamic relations and it is argued that deeper principles might be needed to comprehend the nature of austerity.

A few insights into the nature of classical and quantum gravity via null-strut calculus

Null-strut calculus is a newly developed description of geometrodynamics. It provides a discrete and geometric description of the dynamic evolution or spacelike 3-geometries. Each 3-geometry is distinguished from its neighbours by the everywhere constant value on it of the trace of extrinsic curvature. Each 3-geometry is built out of a simplicial network of quasi-isosceles tetrahedra. These tetrahedra pack together so as to form a piecewise-flat three-dimensional manifold. The authors refer to such a surface as a TET surface. The interior of each tetrahedron of TET is flat Euclidean 3-space. All of the curvature intrinsic to this surface is concentrated at the edge lengths of spacelike structs.

Quantum geometrodynamics of the Bianchi IX cosmological model

The canonical quantum theory of gravity?quantum geometrodynamics (QG)?is applied to the homogeneous Bianchi type IX cosmological model. As a result, a framework for the quantum theory of homogeneous cosmologies is developed. We show that the theory is internally consistent and prove that it possesses the correct classical limit (the theory of general relativity). To emphasize the special role that the constraints play in this new theory, we compare it to the traditional ADM square-root and Wheeler?DeWitt quantization schemes. We show that, unlike traditional approaches, QG leads to a well-defined Schr?dinger equation for the wavefunction of the universe that is inherently coupled to the expectation value of the constraint equations. This coupling to the constraints is responsible for the appearance of a coherent spacetime picture. Thus, the physical meaning of the constraints of the theory is quite different from Diracs interpretation. In light of this distinctive feature of the theory, we re-address the question of the dark energy effects in the Bianchi IX cosmological model for highly non-classical quantum states. We show that, at least for this model, for any choice of the initial wavefunction, quantum corrections will not produce accelerated expansion of the universe.

THE ISSUE OF TIME EVOLUTION IN QUANTUM GRAVITY

We discuss the relation between the concept of time and the dynamic structure of quantum gravity. We briefly review the problems of time associated with the standard procedures of gravity quantization. By explicitly utilizing York’s analysis of the geometrodynamic degrees of freedom, and imposing the constraints as expectation value equations, we describe a new procedure of gravity quantization. In particular, this “minimally constrained canonical” quantization procedure leads to a linear Schrodinger equation augmented by the super-Hamiltonian and supermomentum constraints imposed on expectation values. This approach supplies a description of time evolution in quantum geometrodynamics free from the standard problems of time associated with canonical approaches. Furthermore, the theory is applicable to the full theory of general relativity, without the need to impose symmetries or reduce dimensionality. Using this method we arrive at an analytic expression for the quantum evolution of the Kasner cosmology,...

E. Cartan moment of rotation in Ashtekar's self-dual representation of gravitation

The geometric construction of the E. Cartan moment of rotation associated to the spacetime curvature provides a geometric interpretation of the gravitational field sources and describes geometrically how the sources are ‘‘wired’’ to the field in standard geometrodynamics. The E. Cartan moment of rotation yields an alternate way (as opposed to using variational principles) to obtain Einstein equations. The E. Cartan construction uses, in an essential way, the soldering structure of the frame bundle underlying the geometry of the gravitational field of general relativity. The geometry of Ashtekar’s connection formulation of gravitation is based on a complex‐valued self‐dual connection that is not defined on the frame bundle of spacetime. It is shown how to transfer the construction of the E. Cartan moment of rotation of Ashtekar’s formulation of the theory of gravity and demonstrate that no spurious equations are produced via this procedure.