117256701
Limiting behavior of asymptotically flat gravitational fields
AbstractCouch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that
$$\Psi _0  = O(r^{ - 2 - \varepsilon _0 } )$$
, (d/dr)
$$\Psi _0  = O(r^{ - 3 - \varepsilon _0 } )$$
 and (δ/δxA)
$$\Psi _1  = O(r^{ - 2 - \varepsilon _0 } )$$
, wherexA (A = 2, 3) are angular coordinates, they show that
$$\Psi _1  = O(r^{ - 2 - \varepsilon _1 } )$$
, where ε1⩽ 2 and ε1<ε0;
$$< \varepsilon _0 ;\Psi _2  = O(r^{ - 2 - \varepsilon _2 } )$$
, where ε2 ⩽ 1 and ε1< ε1; and Ψ4 and Ψ3 peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption
$$\Psi _0  = O(r^{ - 3 - \varepsilon _0 } )$$
, (d/dr)
$$\Psi _0  = O(r^{ - 4 - \varepsilon _0 } )$$
, and (δ/δxA)
$$\Psi _0  = O(r^{ - 3 - \varepsilon _0 } )$$
 does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.
35621396
Conserved quantities at spatial and null infinity: The Penrose potential.
We define a superpotential for energy-momentum and rotation momentum which is built out of the conformal tensor and a bivector. This superpotential is identified with that used by Penrose in his definition of quasilocal energy. It is applied to the definition of energy-momentum and rotation momentum at spatial and at null infinities. At spatial infinity the results are in agreement with those of Ashtekar and Hansen. At null infinity the results are unsatisfactory; they are tied to a specific Bondi frame. Thus, they are not in agreement with the results of Tamburino and Winicour, Geroch and Winicour, nor with those of Dray and Streubel. Some reasons for this failure are discussed.
120995906
Degeneracy in loop variables
The small algebra of loop functionals, defined by Rovelli and Smolin, on the Ashtekar phase space of general relativity is studied. Regarded as coordinates on the phase space, the loop functionals become degenerate at certain points. All the degenerate points are found and the corresponding degeneracy is discussed. The intersection of the set of degenerate points with the real slice of the constraint surface is shown to correspond precisely the Goldberg-Kerr solutions. The evolution of the holonomy group of Ashtekar's connection is examined, and the complexification of the holonomy group is shown to be preserved under it. Thus, an observable of the gravitational field is constructed.
13061199
Canonical formalism on a null surface: The scalar and the electromagnetic fields.
The Hamiltonian for the scalar and electromagnetic fields are set up on an outgoing null cone plus that portion of scrI/sup +/ which extends back to space-like infinity. The latter portion is just the energy radiated so that the Hamiltonian is the total energy, a constant of the motion. Because the formalism is set on a characteristic surface, the momenta must satisfy certain constraints in addition to the gauge constraints. These null-surface constraints form a second-class system in the nomenclature of Dirac. Therefore, they are eliminated from the theory by the construction of Dirac brackets. With the Dirac brackets, the Hamiltonian gives the once-integrated field equations for the dynamical field variables. The usual commutation relations for the field strengths restricted to the domain of integration for H are i times the Dirac brackets.
44406528
Generalized Hamilton-Jacobi transformations: Gauge and diffeomorphism constraints.
8115112
Triad approach to the Hamiltonian of general relativity.
The Sparling-Thirring forms are constructed using a connection over a frame bundle defined in terms of a spacelike triad and lapse and shift functions. From the forms, one can identify a first-order Lagrangian from which to construct the Hamiltonian using triad vector densities as basic configuration-space variables. If one uses the self-dual part of the forms, the resulting first-order Lagrangian (its imaginary part is a total divergence) leads to momenta which are the dual of the Sen connection which was introduced by Ashtekar in a spinor representation. The resulting formalism is equivalent to that of Ashtekar.
16978878
What is the statistical significance of the solar neutrino flux problem
Uniform random numbers, not Gaussian random numbers, should have been used with Standard Solar Models to estimate the effect on the neutrino flux of uncertainties in input data. The observed discrepancy is therefore probably quite smaller than currently accepted.
123161968
A new description of high energy antiproton (proton)-proton elastic scattering
Abstract We develop a generalization of the geometric picture for high-energy antiproton (proton)-proton elastic scattering. The eikonal at each impact parameter is considered to have fluctuations about an average value, and is thus characterized by a distribution. A connection to parton branching is made through the specific form of the distribution function for the eikonal. A unified physical theory with significant fluctuations accurately describes the p(p)-p data at both s =546 GeV and 53 GeV. The fluctuation parameter is remarkably well given by that directly observed in multiparticle production.