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.
119857978
ASYMPTOTIC INVARIANTS IN GRAVITATIONAL RADIATION FIELDS
Asymptotic integral invariants are constructed for the electromagnetic and gravitational fields. The integrals are taken over closed two-dimensional surfaces embedded in a null hypersurface. In the absence of incoming radiation the asymptotic behavior of the electromagnetic field F/sup ab/ and the Riemann tensor R/sub abcd/ is such that the integrals formed with these quantities are independent of the particular space-like surface of integration, as long as it lies in the same null hypersurface. Therefore, the integrals are related to the multipole structure of the charge distribution please delete the above abstract no. 31658=====
120204158
Developments and predictions
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.
122157689
Null hypersurfaces and new variables
Following Ashtekar's (1987) recently revised version of the standard canonical theory, the construction of a new variables canonical formalism for Einstein's theory of gravity is investigated when the time parameter has level sets which are null hypersurfaces. The configuration space variables are the components of a tetrad and the self-dual components of a connection. Because a null time parameter is used, the Hamiltonian formalism has second-class constraints as well as the first-class constraints which are associated with the invariance of the theory under diffeomorphisms and local gauge transformations. The first-class constraint algebra is discussed and reality conditions which relate the complex formalism to real general relativity are displayed.
119537735
Newman‐Penrose Constants and Their Invariant Transformations
The origin and significance of the Newman‐Penrose (N‐P) constants of the motion are examined from the point of view that constants of the motion generate invariant transformations. Here the calculation makes use of a generalization of Green's theorem to a situation applicable to the coupled Einstein‐Maxwell fields in general relativity. One finds strictly electromagnetic constants generated by an incoming electromagnetic shock wave, with dipole symmetry, at future null infinity. The gravitational constants contain an admixture from the electromagnetic field. They are generated by an incident quadrupole gravitational shock wave at future null infinity (J+). Both the electromagnetic dipole field and the gravitational quadrupole field behave like linearized fields at J+. All higher‐multipole fields do not uncouple from the nonlinear corrections induced by the self‐coupling of the gravitational field and its coupling with the electromagnetic field. It is shown that the gravitational constants are related to t...
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.