A complex vectorial formalism in general relativity.
Complex vectorial formalism in general relativity, discussing Riemann connection related to representation of Lorentz group by three- dimensional linear space
TENSOR ANALYSIS↗
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The problem of exact interior solutions for rotating rigid bodies in general relativity
The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.
Wahlquist, H. D.↗
On Rosen's theory of gravity and cosmology
Formal similarities between general relativity and Rosen's bimetric theory of gravity were used to analyze various bimetric cosmologies. The following results were found: (1) physically plausible model universes which have a flat static background metric, have a Robertson-Walker fundamental metric, and which allow co-moving coordinates do not exist in bimetric cosmology. (2) it is difficult to use the Robertson-Walker metric for both the background metric (gamma mu nu) and the fundamental metric tensor of Riemannian geometry( g mu nu) and require that g mu nu and gamma mu nu have different time dependences. (3) A consistency relation for using co-moving coordinates in bimetric cosmology was derived. (4) Certain spatially flat bimetric cosmologies of Babala were tested for the presence of particle horizons. (5) An analytic solution for Rosen's k = +1 model was found. (6) Rosen's singularity free k = +1 model arises from what appears to be an arbitary choice for the time dependent part of gamma mu nu.
Barnes, R. C.↗
Coordinate conditions and canonical formalisms in gravitational theory.
Coordinate conditions fix momenta conjugate in Dirac Hamiltonian for general relativity, allowing study of canonical formalism of this theory
DIRAC EQUATION↗
Simultaneous two component squeezing in generalized q-coherent states
Using a generalization of the q-commutation relations, we develop a formalism in which it is possible to define generalized q-bosonic operators. This formalism includes both types of the usual q-deformed bosons as special cases. The coherent states of these operators show interesting and novel noise reduction properties including simultaneous squeezing in both field components, unlike the conventional case in which squeezing is permitted in only one component. This also contrasts with the usual quantum group deformation which also only permits one component squeezing.
Mcdermott, Roger J.↗
Corrections to the thin wall approximation in general relativity
The question is considered whether the thin wall formalism of Israel applies to the gravitating domain walls of a lambda phi(exp 4) theory. The coupled Einstein-scalar equations that describe the thick gravitating wall are expanded in powers of the thickness of the wall. The solutions of the zeroth order equations reproduce the results of the usual Israel thin wall approximation for domain walls. The solutions of the first order equations provide corrections to the expressions for the stress-energy of the wall and to the Israel thin wall equations. The modified thin wall equations are then used to treat the motion of spherical and planar domain walls.
Garfinkle, David↗
Dipole-field sums and Lorentz factors for orthorhombic lattices, and implications for polarizable molecules
A method for computing the Lorentz tensor components in single crystals via rapidly convergent sums of Bessels functions is developed using the relationship between dipole-field sums and the tensor components. The Lorentz factors for simple, body-centered, and base-centered orthorhombic lattices are computed using this method, and the derivative Lorentz factors for simple orthorhombic lattices are also determined. Both the Lorentz factors and their derivatives are shown to be very sensitive to a lattice structure. The equivalent of the Clausius-Mossotti relation for general orthorhombic lattices is derived using the Lorentz-factor formalism, and the permanent molecular dipole moment is related to crystal polarization for the case of a ferroelectric of polarizable point dipoles. It is concluded that the polarization enhancement due to self-polarization familiar from classical theory may actually be a reduction in consequences of negative Lorentz factors in one or two lattice directions for noncubic crystals.
Purvis, C. K.↗
Applications of Formal Methods to Specification and Safety of Avionics Software
This report treats several topics in applications of formal methods to avionics software development. Most of these topics concern decision tables, an orderly, easy-to-understand format for formally specifying complex choices among alternative courses of action. The topics relating to decision tables include: generalizations fo decision tables that are more concise and support the use of decision tables in a refinement-based formal software development process; a formalism for systems of decision tables with behaviors; an exposition of Parnas tables for users of decision tables; and test coverage criteria and decision tables. We outline features of a revised version of ORA's decision table tool, Tablewise, which will support many of the new ideas described in this report. We also survey formal safety analysis of specifications and software.
Hoover, D. N.↗
Kruskal space and the uniformly accelerated frame.
Kruskal space in general relativity and uniform accelerated rigid rod in special relativity show striking formal similarities
SIMILARITY HYPOTHESIS↗
Sonic boom measurement test plan for Space Shuttle STS-4 reentry
Formal documentation for measurement procedures and system specifications, and general information relating to the Space Shuttle STS-4 Sonic Boom Measurement Program are supplied. This test plan is designed to provide information, guidance, and assignment of responsibilities for the acquisition of sonic boom and atmospheric measurements, timing correlation, communications and other necessary supporting tasks. Specifically included are details such as mobile data acquisition station locations, measurement systems calibration levels, predicted sonic boom overpressure levels, overpressure level assignment for each data acquisition station, data recording times on and off, universal coordinated time, and measurement system descriptions.
Henderson, H. R.↗
Noisy bases in Hilbert space: A new class of thermal coherent states and their properties
Coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, are introduced as a 'random' (or 'thermal' or 'noisy') basis in Hilbert space. A resolution of the identity for these states is proved and used to generalize the usual coherent state formalism for the finite temperature case. The Bargmann representation of an operator is introduced and its relation to the P and Q representations is studied. Generalized P and Q representations for the finite temperature case are also considered and several interesting relations among them are derived.
Vourdas, A.↗
Sonic boom measurement test plan for Space Shuttle STS-1 reentry
Formal documentation for measurement procedures and system specifications, and general information are relating to the Space Shuttle STS-1 Sonic Boom Measurement Program are supplied. This test plan is designed to provide information, guidance, and assignment of responsibilities for the acquisition of sonic boom and atmospheric measurements, timing correlation, communications and other necessary supporting tasks. Specifically included are details such as mobile data acquisition station locations, measurement systems calibration levels, predicted sonic boom overpressure levels, overpressure level assignment for each data acquisition station, data recording times on and off, universal coordinated time, and measurement system descriptions.
Henderson, H. R.↗
Kinetic theory of turbulent compressible flows and comparison with classical theory
A complete set of turbulent correlations is given in terms of expansion coefficients in a double series of Hermite polynomials of a two-particle correlation in phase space. Only two of these coefficients, corresponding to Reynolds stress and turbulent heat flux, are shown to appear in gasdynamic equations of turbulence. This is accomplished by incorporating the phase-space correlation in the collision integral of Boltzmann's equation and by deriving generalized Navier-Stokes and Fourier transport relations. In contrast to the classical formalism, the simple expression remains invariant in form whether the flow is compressible or not. Nevertheless, a bilinear transformation of fluctuating quantities shows that the two formalisms are identical with regard to terms of double correlations. The kinetic theory justifies nonexistence of the higher-order correlations characteristic of compressible-turbulence equations in the classical regime.
Tsuge, S.↗
The application of the principles of invariance to the radiative transfer equation in plant canopies
Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.
Ganapol, B. D.↗
NASA publications manual 1974
The various types of NASA publications are described, including formal series, contributions to external publications, informal papers, and supplementary report material. The physical appearance and reproduction procedures for the format of the NASA formal series are discussed, and samples are provided. Matters relating to organization, content, and general style are also considered.
Source record↗
The relativistic equations of stellar structure and evolution
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. A general relativistic version of the mixing-length formalism for convection is presented. It is argued that in work on spherical systems, general relativity theorists have identified the wrong quantity as total mass-energy inside radius r.
Thorne, K. S.↗
Teleparallelism as a universal connection on null hypersurfaces in general relativity
It is shown that a close relationship between the inner geometry of a null hypersurface N3 and the Newman-Penrose (NP) (1962, 1963) spin coefficient formalism exists. Projecting the null complex NP tetrad onto N3, two triads of basis vectors in N3 are obtained. The inner geometry of N3 is based on the assumption that these vectors are parallelly transported along the surface; this gives rise to the teleparallel connection as a metric nonsymmetric affine connection. The gauge freedom for the choice of the basis triads is given by the isotropy subgroup of the local Lorentz group leaving invariant the direction of the null generators of N3, and teleparallelism is determined by the equivalence class of the basis triads with respect to the global gauge group. Nine of the twelve NP coefficients are identified as the triad components of the torsion and the second fundamental form of N3. The resulting generalized Gauss-Codazzi equations are identical to nine of the NP equations, i.e., to the half of the Ricci identities. This result gives a geometrical meaning to the entire formalism. Finally a general proof of Penrose's theorem that the shear of the null generators of N3 is the only initial null datum for a gravitational field on N3 is presented.
Mazur, P. O.↗
The relativistic equations of stellar structure and evolution. Stars with degenerate neutron cores. 1: Structure of equilibrium models
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."
Thorne, K. S.↗