120204158
Developments and predictions
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.
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...
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.
44406528
Generalized Hamilton-Jacobi transformations: Gauge and diffeomorphism constraints.
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.
119498503
Baryonic Dark Matter and Big-Bang Nucleosynthesis
The enclosed paper was submitted for publication in Ap.J Lett. in February 1992. It has been rejected on the grounds that it predicts primordial Deuterium abundance which is contradicted by observations and because it disagreed with published analysis and conclusions of previous authors. However, in a recent article in NATURE (14 April 1994) Vol. 368 pp. 599-603, Songalia, Cowie, Hogan and Rugers describe a recent measurement (November 1993) with the Keck 10-m Telescope, of the Deuterium abundance in a high redshift cloud between us and a distant quasar. They find D/H\approx 1.9-2.5 x10^{-4} in good agreement with our prediction D/H=(2.1+\- 0.35)x10^{-4}, which is larger by an order of magnitude than believed before. Songalia et al. found that the baryon density inferred from Big Bang Nucleosynthesis is "consistent with the amount of presently observed luminous matter comprising all the baryons in the Universe" while we found the same. We post here our unpublished 1991 paper, which was reported in international conferences and was distributed only as a preprint, mainly because of its physics and its sad moral: If you submit for publication a correct paper with important results that contradict the "party line" it has only slim chances to be accepted for publication.
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.