Gravitational Constraint Combinations Generate a Lie Algebra

We find a first--order partial differential equation whose solutions are all ultralocal scalar combinations of gravitational constraints with Abelian Poisson brackets between themselves. This is a generalisation of the Kucha\v{r} idea of finding alternative constraints for canonical gravity. The new scalars may be used in place of the hamiltonian constraint of general relativity and, together with the usual momentum constraints, replace the Dirac algebra for pure gravity with a true Lie algebra: the semidirect product of the Abelian algebra of the new constraint combinations with the algebra of spatial diffeomorphisms.Comment: 10 pages, latex, submitted to Classical and Quantum Gravity. Section 3 is expanded and an additional solution provided, minor errors correcte

Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra

We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the usual Hamiltonian constraint by alternative combinations of the gravitational constraints (scalar densities of arbitrary weight), whose Poisson brackets strongly vanish and cast the standard constraint-system for vacuum gravity into a form that generates a true Lie algebra. It is shown that any such combination---that satisfies certain reality conditions---may be derived from an action principle involving a single scalar field and a single Lagrange multiplier with a non--derivative coupling to gravity.Comment: 26 pages, plain TE

Canonical Formulation of pp-waves

We construct a Hamiltonian formulation for the class of plane-fronted gravitational waves with parallel rays (pp-waves). Because of the existence of a light-like Killing vector, the dynamics is effectively reduced to a 2+1 evolution with "time" chosen to be light-like. In spite of the vanishing action this allows us to geometrically identify a symplectic form as well as dynamical Hamiltonian, thus casting the system into canonical form.Comment: To appear in the "Obregon Festschrift

The impact of ventilation type on the heat load of dairy cows

Received: January 31st, 2021 ; Accepted: March 27th, 2021 ; Published: November 26th, 2021 ; Correspondence: [email protected] load in cattle causes deterioration of health and reduced production of milk. Therefore, it is necessary to protect cows by appropriate passive and active means and monitor the air quality in barns. Based on several indicators of environmental quality, is possible to make a more comprehensive assessment of the microclimate and more precise conclusions. This study, was monitoring the values of air temperature, relative humidity, and air velocity in two barns with the same volume and layout with floor dimensions of 26.6 m × 62.1 m. In barn 1, roof ridge of which had underwent only partial reconstruction, there were installed fourteen basket fans with a total fan performance Q(1)fans = 218,400 m3 h -1 . In barn 2, there were twelve panel fans with a total fan performance Q(2)fans = 289,320 m3 h -1 . The resulting THI, HLI and ETIC values were compared in relation to each other and in relation to the recommended values. Despite the operating ventilation technology and enlargement of wall openings, the above-limit values of climatic characteristics were observed in both barns during tropical days. There were no differences between the barns (p ˃ 0.05), in barn 1: THI(1) = 83.10 ± 0.51; HLI(1) = 85.62 ± 1.42; ETIC(1) = 27.24 ± 0.31, and in barn 2: THI(2) = 83.12 ± 0.34; HLI(2) = 85.77 ± 1.50; ETIC(2) = 27.29 ± 0.28, however, there were found significant differences in values of temperature indices obtained in the detailed measurements at points arranged perpendicularly, as well as parallelly, to the direction of air velocity in the animal zone (p < 0.05)

Geometric Bounds in Spherically Symmetric General Relativity

We exploit an arbitrary extrinsic time foliation of spacetime to solve the constraints in spherically symmetric general relativity. Among such foliations there is a one parameter family, linear and homogeneous in the extrinsic curvature, which permit the momentum constraint to be solved exactly. This family includes, as special cases, the extrinsic time gauges that have been exploited in the past. These foliations have the property that the extrinsic curvature is spacelike with respect to the the spherically symmetric superspace metric. What is remarkable is that the linearity can be relaxed at no essential extra cost which permits us to isolate a large non - pathological dense subset of all extrinsic time foliations. We identify properties of solutions which are independent of the particular foliation within this subset. When the geometry is regular, we can place spatially invariant numerical bounds on the values of both the spatial and the temporal gradients of the scalar areal radius, $R$. These bounds are entirely independent of the particular gauge and of the magnitude of the sources. When singularities occur, we demonstrate that the geometry behaves in a universal way in the neighborhood of the singularity.Comment: 16 pages, revtex, submitted to Phys. Rev.

General relativity histories theory II: Invariance groups

We show in detail how the histories description of general relativity carries representations of both the spacetime diffeomorphisms group and the Dirac algebra of constraints. We show that the introduction of metric-dependent equivariant foliations leads to the crucial result that the canonical constraints are invariant under the action of spacetime diffeomorphisms. Furthermore, there exists a representation of the group of generalised spacetime mappings that are functionals of the four-metric: this is a spacetime analogue of the group originally defined by Bergmann and Komar in the context of the canonical formulation of general relativity. Finally, we discuss the possible directions for the quantization of gravity in histories theory.Comment: 24 pages, submitted to Class. Quant. Gra

Canonical Gravity, Diffeomorphisms and Objective Histories

This paper discusses the implementation of diffeomorphism invariance in purely Hamiltonian formulations of General Relativity. We observe that, if a constrained Hamiltonian formulation derives from a manifestly covariant Lagrangian, the diffeomorphism invariance of the Lagrangian results in the following properties of the constrained Hamiltonian theory: the diffeomorphisms are generated by constraints on the phase space so that a) The algebra of the generators reflects the algebra of the diffeomorphism group. b) The Poisson brackets of the basic fields with the generators reflects the space-time transformation properties of these basic fields. This suggests that in a purely Hamiltonian approach the requirement of diffeomorphism invariance should be interpreted to include b) and not just a) as one might naively suppose. Giving up b) amounts to giving up objective histories, even at the classical level. This observation has implications for Loop Quantum Gravity which are spelled out in a companion paper. We also describe an analogy between canonical gravity and Relativistic particle dynamics to illustrate our main point.Comment: Latex 16 Pages, no figures, revised in the light of referees' comments, accepted for publication in Classical and Quantum Gravit

Time evolution and observables in constrained systems

The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework. The existence of reasonable true, or physical, degrees of freedom is rigorously defined and called {\em local reducibility}. A proof is given that any locally reducible system admits a complete set of perennials. For locally reducible systems, the most general construction of time evolution in the Schroedinger and Heisenberg form that uses only geometry of the phase space is described. The time shifts are not required to be 1symmetries. A relation between perennials and observables of the Schroedinger or Heisenberg type results: such observables can be identified with certain classes of perennials and the structure of the classes depends on the time evolution. The time evolution between two non-global transversal surfaces is studied. The problem is posed and solved within the framework of the ordinary quantum mechanics. The resulting non-unitarity is different from that known in the field theory (Hawking effect): state norms need not be preserved so that the system can be lost during the evolution of this kind.Comment: 31 pages, Latex fil

Turbofan mixed flow exhaust system

An improved exhaust system including a lobed mixer and an improved exhaust centerbody is provided. The improved exhaust centerbody includes means for cooperating with the lobed mixer to increase mixing effectiveness of the exhaust system without substantially increasing pressure losses attributable thereto. In a preferred embodiment of the invention, the cooperating means include a plurality of circumferentially spaced elongated deformations, such as grooves and ridges, which deformations extend radially with respect to a reference surface of the exhaust centerbody and which deformations are aligned in an axial direction substantially parallel to a longitudinal axis of the centerbody