General structure of the solutions of the Hamiltonian constraints of gravity

A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some cases. A starting point for the systematic study of the solutions of Einstein gravity is suggested.Comment: 17 pages, LaTeX, submitted to International J. of Geom. Meth. in Modern Physics. Added comments in the last sectio

Test Matter in a Spacetime with Nonmetricity

Examples in which spacetime might become non-Riemannian appear above Planck energies in string theory or, in the very early universe, in the inflationary model. The simplest such geometry is metric-affine geometry, in which {\it nonmetricity} appears as a field strength, side by side with curvature and torsion. In matter, the shear and dilation currents couple to nonmetricity, and they are its sources. After reviewing the equations of motion and the Noether identities, we study two recent vacuum solutions of the metric-affine gauge theory of gravity. We then use the values of the nonmetricity in these solutions to study the motion of the appropriate test-matter. As a Regge-trajectory like hadronic excitation band, the test matter is endowed with shear degrees of freedom and described by a world spinor.Comment: 14 pages, file in late

The Husain-Kuchar Model: Time Variables and Non-degenerate Metrics

We study the Husain-Kuchar model by introducing a new action principle similar to the self-dual action used in the Ashtekar variables approach to Quantum Gravity. This new action has several interesting features; among them, the presence of a scalar time variable that allows the definition of geometric observables without adding new degrees of freedom, the appearance of a natural non-degenerate four-metric and the possibility of coupling ordinary matter.Comment: LaTeX, 22 pages, accepted for publication in Phys. Rev.

Non-Linear Affine Embedding of the Dirac Field from the Multiplicity-Free SL(4,R) Unirreps

The correspondence between the linear multiplicity-free unirreps of SL(4, R) studied by Ne'eman and {\~{S}}ija{\~{c}}ki and the non-linear realizations of the affine group is worked out. The results obtained clarify the inclusion of spinorial fields in a non-linear affine gauge theory of gravitation.Comment: 13 pages, plain TeX, macros include

Growth hormone and aging

Les alteracions vasculars i degeneratives del sistema nerviós central (SNC) són dues de les causes més comunes de malaltia i de mort entre la gent gran; ambdues es correlacionen amb l'edat, amb la deficiència en GH, i poden afectar les funcions fisiològiques de la població d'edat avançada. Amb la finalitat de clarificar els efectes de la GH en el metabolisme, en els vasos i en el SNC, hem dut a terme un estudi in vivo utilitzant rates vellesWistar tractades crònicament amb GH. Les rates velles varen presentar un augment en el pes de greix i una disminució de l'índex específic de gravetat (SGI) (p < 0,05) en comparar-les amb les rates adultes no tractades. La GH va reduir el pes en greix (p < 0,05), i va mostrar també una tendència a augmentar l'SGI. Es va analitzar també la resposta de diverses substàncies vasoactives en els anells aòrtics, i es va demostrar una disminució de la vasodilatació per acetilcolina i isoprenalina (p < 0,05) en els animals vells. La contracció induïda per acetilcolina+L-NAME era més alta en els animals vells que en els adults. L'administració de GH millorava les respostes vasodilatadores (p < 0,05) mentre que tendia a reduïr les respostes vasoconstrictores. L'àrea aòrtica mitja augmentava també en les rates velles, mentre que la GH reduïa aquest paràmetre (p < 0,05). Les poblacions neuronals es reduïen en els hipocamps de les rates velles en comparar-les amb les joves. Aquesta reducció estava asociada a un augment dels nucleosomes i a una reducció de Bcl2 en el cervell. Les caspases 3 i 9 també varen augmentar. El tractament amb GH va augmentar significativament el nombre de neurones i va reduir els nucleosomes i les caspases i augmentar el Bcl2. En conclusió, el tractament perGHindueix l'aparició d'efectes beneficiosos en la composició del cos i ha restablert també les funcions cerebrals i vasculars en les rates velles.Vascular and degenerative alterations of the central nervous system (CNS) are two of the most common reasons for illness and death in elderly people; they exhibit an age-related GH deficiency that can affect their physiological functions. A study was conducted under chronic in vivo conditions using old Wistar rats, in order to clarify the effects of GH on the metabolism, vessels, and the CNS. The old rats showed an increased fat weight and a decreased Specific Gravity Index (SGI) (p < 0.05), as compared to the adult animals. GH reduced the fat weight (p < 0.05) and tended to increase the SGI (N.S.). The response to several vasoactive substances in aortic rings showed impaired vasodilatation to Acetylcholine and Isoprenaline (p < 0.05) in the old animals. Contraction, induced by Acetylcholine+ L-NAME, was higher in the old rats than in the adults. GH administration improved the vasodilatory responses (p < 0.05) and tended to reduce the constrictory responses. The aortic media area was increased in the old rats, and GH reduced this parameter (p < 0.05). The neuronal populations were reduced in the hippocampi of the old rats as compared to the young ones. This reduction was associated with an increase in nucleosomes and a reduction in Bcl2 in the brain. An increase was also detected in caspases 3 and 9. GH treatment was able to significantly enhance the number of neurons by reducing the nucleosomes and the caspases and by increasing Bcl2. In conclusion,GHtreatment was able to show beneficial effects on body composition and was able to restore both vascular and brain functions in the old rats

Hamiltonian Poincar\'e Gauge Theory of Gravitation

We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as the local spacetime group of the gravitational gauge theory, with $SO(3)$ as the classification subgroup. The Wigner--like rotation induced by the nonlinear approach singularizes out the role of time and allows to deal with ordinary $SO(3)$ vectors. We apply the general results to the Einstein--Cartan action. We study the constraints and we obtain Einstein's classical equations in the extremely simple form of time evolution equations of the coframe. As a consequence of our approach, we identify the gauge--theoretical origin of the Ashtekar variables.Comment: 38 pages, plainTe

Black Holes with Weyl Charge and Non-Riemannian Waves

A simple modification to Einstein's theory of gravity in terms of a non-Riemannian connection is examined. A new tensor-variational approach yields field equations that possess a covariance similar to the gauge covariance of electromagnetism. These equations are shown to possess solutions analogous to those found in the Einstein-Maxwell system. In particular one finds gravi-electric and gravi-magnetic charges contributing to a spherically symmetric static Reissner-Nordstr\"om metric. Such Weyl ``charges'' provide a source for the non-Riemannian torsion and metric gradient fields instead of the electromagnetic field. The theory suggests that matter may be endowed with gravitational charges that couple to gravity in a manner analogous to electromagnetic couplings in an electromagnetic field. The nature of gravitational coupling to spinor matter in this theory is also investigated and a solution exhibiting a plane-symmetric gravitational metric wave coupled via non-Riemannian waves to a propagating spinor field is presented.Comment: 18 pages Plain Tex (No Figures), Classical and Quantum Gravit

Dark Matter Gravitational Interactions

We argue that the conjectured dark mater in the Universe may be endowed with a new kind of gravitational charge that couples to a short range gravitational interaction mediated by a massive vector field. A model is constructed that assimilates this concept into ideas of current inflationary cosmology. The model is also consistent with the observed behaviour of galactic rotation curves according to Newtonian dynamics. The essential idea is that stars composed of ordinary (as opposed to dark matter) experience Newtonian forces due to the presence of an all pervading background of massive gravitationally charged cold dark matter. The novel gravitational interactions are predicted to have a significant influence on pre-inflationary cosmology. The precise details depend on the nature of a gravitational Proca interaction and the description of matter. A gravitational Proca field configuration that gives rise to attractive forces between dark matter charges of like polarity exhibits homogeneous isotropic eternal cosmologies that are free of cosmological curvature singularities thus eliminating the horizon problem associated with the standard big-bang scenario. Such solutions do however admit dense hot pre-inflationary epochs each with a characteristic scale factor that may be correlated with the dark matter density in the current era of expansion. The model is based on a theory in which a modification of Einsteinian gravity at very short distances can be expressed in terms of the gradient of the Einstein metric and the torsion of a non-Riemannian connection on the bundle of linear frames over spacetime. Indeed we demonstrate that the genesis of the model resides in a remarkable simplification that occurs when one analyses the variational equations associated with a broad class of non-Riemannian actions.Comment: 40 pages, 4 Postscript figure

Towards complete integrability of two dimensional Poincar\'e gauge gravity

It is shown that gravity on the line can be described by the two dimensional (2D) Hilbert-Einstein Lagrangian supplemented by a kinetic term for the coframe and a translational {\it boundary} term. The resulting model is equivalent to a Yang-Mills theory of local {\it translations} and frozen Lorentz gauge degrees. We will show that this restricted Poincar\'e gauge model in 2 dimensions is completely integrable. {\it Exact} wave, charged black hole, and `dilaton' solutions are then readily found. In vacuum, the integrability of the {\it general} 2D Poincar\'e gauge theory is formally proved along the same line of reasoning.Comment: 35 pages, report Cologne-thp-1993-H