Cartan and relativistic spin fluids in a rotating cylinder
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Krisch, J. P.↗
Engineering topics
Smalley, L. L.
Publications and source records attributed to Smalley, L. L..
Brans-Dicke-type models with nonmetricity
A scalar-tensor-nonmetric theory of gravity without matter fields is shown to be equivalent to the scalar-tensor-torsion theory proposed by German, the only difference being in the source of the Weyl vector or torsion vector (for equivalently the scalar field) which remains arbitrary in the theory. General extended conformal transformations, which leave the curvature tensor invariant, are presented and their implications for metric-affine theories and scalar-tensor theories are discussed.
Smalley, L. L.↗
Geometrization of spin and the Weyssenhoff fluid conjecture
It is shown that the logical treatment of spinning perfect fluids occurs in a metric-torsion space-time with or without mass conservation. The Lagrangian formulation of a spin density fluid is reviewed, concentrating on the relationship between spin and torsion for metric-torsion space-times. The significance of the mass constraint is discussed, and its consequences for the variation of the Lagrangian is given. That consequence is the geometrization of spin; that is, the Weyssenhoff form relating spin and the trace-free torsion is obtained without any ad hoc assumption.
Smalley, L. L.↗
Discrete Dirac equation on a finite half-integer lattice
The formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.
Smalley, L. L.↗
Self-consistent Goedel cosmology with spin-density in Riemann-Cartan spacetime
It is shown that the Goedel metric (GM) for a rotating cosmology is compatible with the self-consistent formulation of the Einstein-Cartan (EC) metric-torsion theory for a spinning fluid. The proposed calculation shows, within the context of an EC theory, how to self-consistently incorporate a perfect fluid with spin density into the GM without changing the metric. It is found that the only changes produced in the GM parameters in connection with a spinning fluid are that the cosmological constant becomes slightly more negative and the sense of rotation is flipped 180 deg.
Smalley, L. L.↗
Goedel cosmology in Riemann-Cartan spacetime with spin density
It is shown that the Goedel metric for a rotating cosmology is compatible with the self-consistent formulation of the Einstein-Cartan metric-torsion theory for a spinning fluid. In the model presented, the only changes are that the cosmological constant becomes slightly more negative, and the sense of rotation is flipped. If the Goedel model were a viable model, experimentally it would be difficult to distinguish between the two models unless the spin density could be measured directly.
Smalley, L. L.↗
Variational principle for a prototype Rastall theory of gravitation
A prototype of Rastall's theory of gravity, in which the divergence of the energy-momentum tensor is proportional to the gradient of the scalar curvature, is shown to be derivable from a variational principle. Both the proportionality factor and the unrenormalized gravitational constant are found to be covariantly constant, but not necessarily constant. The prototype theory is, therefore, a gravitational theory with variable gravitational constant.
Smalley, L. L.↗
Riemann Curvature tensor in nonholonomic coordinates and non-Riemannian space-times
The calculation of the Riemann Curvature from the deviation of a vector undergoing parallel transport around a closed loop takes a very simple form when expressed in generalized geometrical notation. The parallel transport of a vector and the type of closed loop used in the calculation are discussed. The method generalizes similar work of Morganstern (1977) to nonholonomic coordinates and non-Riemannian space-times.
Smalley, L. L.↗
Rastall's and related theories are conservative gravitational theories although physically inequivalent to general relativity
The proper framework for testing Rastall's theory and its generalizations is in the case of non-negligible (i.e. discernible) gravitational effects such as gravity gradients. These theories have conserved integral four-momentum and angular momentum. The Nordtvedt effect then provides limits on the parameters which arise as the result of the non-zero divergence of the energy-momentum tensor.
Smalley, L. L.↗
Spinning fluids in the Einstein-Cartan theory
An Eulerian variational principle for a spinning fluid in the Einstein-Cartan metric-torsion theory is presented. The variational principle yields the complete set of field equations for the system. The symmetric energy-momentum tensor is a sum of a perfect-fluid term and a spin term.
Ray, J. R.↗
Spinning fluids in general relativity
General relativity field equations are employed to examine a continuous medium with internal spin. A variational principle formerly applied in the special relativity case is extended to the general relativity case, using a tetrad to express the spin density and the four-velocity of the fluid. An energy-momentum tensor is subsequently defined for a spinning fluid. The equations of motion of the fluid are suggested to be useful in analytical studies of galaxies, for anisotropic Bianchi universes, and for turbulent eddies.
Ray, J. R.↗
Improved perfect-fluid energy-momentum tensor with spin in Einstein-Cartan space-time
The description of the spin given here is classical in that it is intrinsic but not quantized. The approach in this matter is similar to, for example, the work of Bailey and Israel (1973, 1975, 1979), where the fluid particles, which have intrinsic spin, may be galaxies or clusters of galaxies. The elementary particles of these objects and the 'ferromagnetic alignment' of their quantum spins are not resorted to in order to describe a fluid with spin. Physically this means that the equation of motion for the spin tensor is a modified Fermi-Walker transport equation (Misner et al., 1973), arising as a direct result of the inclusion of spin as an intrinsic variable in the thermodynamic description of the internal energy. The variables in this description are classical variables throughout and are not microscopic fields. An improved perfect-fluid energy-momentum tensor that includes spin and torsion is presented. Use is made of a Lagrangian variational principle based on the tetrad formalism of Halbwach (1960) and the method od constraints of Ray (1972).
Ray, J. R.↗
Can Malin's gravitational-field equations be modified to obtain a viable theory of gravity
Malin's (1975) gravitational theory, which was recently shown by Lindblom and Nester (1975) to be incorrect, is modified by means of a recently proposed method for obtaining viable gravitational theories. The resulting self-consistent theory, which is in effect a Rastall-type modification of the Einstein theory, exhibits nonconservation of momentum, yet agrees with all experimental limits known to date within the post-Newtonian approximation framework.
Smalley, L. L.↗
Scalar-tensor theory of gravitation with negative coupling constant
The possibility of a Brans-Dicke scalar-tensor gravitation theory with a negative coupling constant is considered. The admissibility of a negative-coupling theory is investigated, and a simplified cosmological solution is obtained which allows a negative derivative of the gravitation constant. It is concluded that a Brans-Dicke theory with a negative coupling constant can be a viable alternative to general relativity and that a large negative value for the coupling constant seems to bring the original scalar-tensor theory into close agreement with perihelion-precession results in view of recent observations of small solar oblateness.
Smalley, L. L.↗
Gravitational theories with nonzero divergence of the energy-momentum tensor
Assuming that the divergence of the energy-momentum tensor is nonzero leads to a class of theories with consistent field equations and gauge conditions as well as compatibility with the Newtonian limit of the conservation laws. Both the Einstein and the Brans-Dicke theories are used as models, but the extension to other viable theories such as vector-metric and two-metric theories is possible. One particularly interesting theory emerges that agrees with the ordinary Brans-Dicke theory except for the post-Newtonian parameter zeta sub 2, which predicts nonconservation of total momentum. Unfortunately, no accurate experimental limits for this parameter are known. It thus remains for future experiments in lunar-laser ranging to test this theory.
Smalley, L. L.↗
Gravitational clock: A proposed experiment for the measurement of the gravitational constant G
The increased importance and the fundamental significance of accurately measuring the gravitational constant G are discussed along with recent or proposed experimental measurements of G. The method of using mutually gravitating bodies in the clock mode in a drag-free satellite is described. A satellite experiment consisting of the flat-plate spherical mass oscillator proposed combines the mathematical and experimental conveniences most simply. It is estimated that accuracies of 1 part in 1,000,000 are easily obtainable by careful fabrication of parts. The use of cryogenic techniques, thin films, and superconductors allows increased accuracies of two or three orders of magnitude or better. These measurements can be increased to the level of 1 part in 10 to the 11th power at which time-variations, and other variations, in G can be observed.
Smalley, L. L.↗
Relativistic astrophysics
The coordinate independence of gravitational radiation and the parameterized post-Newtonian approximation from which it is extended are described. The general consistency of the field equations with Bianchi identities, gauge conditions, and the Newtonian limit of the perfect fluid equations of hydrodynamics are studied. A technique of modification is indicated for application to vector-metric or double metric theories, as well as to scalar-tensor theories.
Smalley, L. L.↗
Do massive Brans-Dicke theories of gravitation imitate Brans-Dicke theories with nonzero divergence of energy-momentum tensor
Acharya and Hogan (1973) have introduced a massive scalar field into the usual Brans-Dicke (1961) theory of gravitation. Formally they obtain certain field equations. The assumption of a nonzero divergence for T mu nu (or equivalently the introduction of sources) formally imitates a massive Brans-Dicke and satisfies the condition of Acharya and Hogan that the theory be indistinguishable with the classical test of the Einstein theory. Although it was shown elsewhere that the modified Brans-Dicke theory agrees with the classical test under certain conditions, there were no specified limits on omega, a similar circumstance discovered by Acharya and Hogan for the massive scalar field.
Smalley, L. L.↗