Extrinsic curvature for the two-black-hole problem

The solutions of the momentum constraints on the Einstein-Rosen manifold with two bridges, representing two black holes, are analyzed. These solutions are in the form of an infinite series. Their higher order terms are shown to fall off asr ^–6. These terms add multipole moments and gravitational radiation to the initial data and do not contribute to the linear and (spin) angular momenta of the black holes.     

Toward a canonical formalism of non-perturbative two-dimensional gravity

On the basis of the previously proposed action principle describing the theory space of 2D gravity in less than one-dimension, we develop a systematic canonical formalism for studying the properties of the string equation in the phase space of the cosmological constant and its canonical conjugate, the puncture operator. The string equation is written in a manifestly invariant form under the group of regular canonical transformations in the phase space of generalized coordinate and momentum. As a consequence, the geometrical origin of the generalized Virasoro condition on the partition function (or more precisely, the -function) is understood to be the symmetry under the regular area-preserving diffeomorphisms (w ₁₊ symmetry) in the deformed phase space. The deformed canonical formalism can be regarded as a quantization of a classical canonical formalism describing the sphere limit of the theory.     

Covariant canonical formalism for gravity

We continue the previous discussion (A. D'Adda, J. E. Nelson, and T. Regge, Ann. Phys. (N.Y.)165) of the covariant canonical formalism for the group manifold and relate it to the standard canonical vierbein formalism as pioneered by Dirac. The form bracket is related to the Poisson bracket of classical mechanics. We utilise systematically the calculus of differential forms and a compound notation which labels Poincaré multiplets. In this way we obtain a particularly clear and compact expression for the Hamiltonian and the constraints algebra of the vierbein formalism.     

Geometry of canonical variables in gravity theories

We show how to pass from an SL(2, C) covariant to an SU(2) covariant formulation of the theories of gravity. Our construction determines the canonical and gauge variables of the theory and establishes an appropriate framework for a hamiltonian picture.     

Fixed-focal-axis solar concentrators with a curvature determined by gravity

Summary Solar concentrators with East-West axis, curvature determined by force of gravity and a fixed focal axis have been analysed and compared, both from the standpoint of the general technical aspects, as the different position of the focal axis, and from the standpoint of the working ability that they can supply: concentration factor and quantity of energy transmitted to the collector.

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Riassunto Concentratori solari con asse est-ovest, curvatura determinata dalla forza di gravità e asse focale fisso sono analizzati e confrontati sia dal punto di vista degli aspetti tecnici generali, come la diversa posizione dell'asse focale, sia dal punto di vista delle prestazioni che possono fornire: fattore di concentrazione e quantità di energia trasmessa al collettore.

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Резюме Проводится анализ солнечных концентраторов с осью вдоль направления ?восток-запад?, имеющих кривизну, которая определяется силой гравитации, и с фиксированной фокальной осью. Анализ проводится с точки зрения общетехнических аспектов, таких как различное положение фокальной оси, а также с точки зрения фактора концентрации и величины энергии, передаваемой на коллектор.

     

Field equations for gravity quadratic in the curvature

Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian—namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type—is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differ from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built.