Larry L. Smalley

Geometrization of spin and the Weyssenhoff fluid conjecture

We show that the logical treatment of spinning perfect fluids occurs in a metrictorsion space-time with or without mass conservation. The consequence is the geometrization of spin; that is, we obtain the Weyssenhoff form relating spin and the trace-free torsion without any ad hoc assumption.

Self-consistent Gödel cosmology with spin-density in Riemann-Cartan spacetime

Abstract We show that the Godel metric for a rotating cosmology is compatible with the self-consistent formulation of the Einstein-Cartan metric-torsion theory for a spinning fluid.

On the extension of geometric optics from Riemannian to Riemann-Cartan spacetime

Abstract In the extension to Riemann-Cartan spacetime, the optical properties of electromagnetic waves are found to depend strongly on the nature of the Lorentz gauge condition. If the Lorentz gauge condition is treated similar to the non-minimal extension of the electromagnetic field to Riemann-Cartan spacetime, then the optical properties of waves are identical to those in riemannian spacetime. If the gauge is treated as an intrinsically Riemann-Cartan condition, then, to the same order of approximation, the optical properties of waves remain the same, except that the polarization vector is no longer parallel propagated along the wave vector.

On the lagrangian formulation of spinning fluids in Riemann-Cartan spacetime

Abstract We consider the problems of obtaining a well-defined, explicit, lagrangian formulation in curved spacetime for perfect fluids with spin density.

Spin fluids in van Stockum cylinders

Within general relativity, the stress-energy content of van Stockums two- dimensional dust interior is extended to include a two-dimensional spin fluid. The metric and spin-fluid parameters are expressed in terms of one generating function. As an application, a rotating cloud of spin fluid is discussed.

The Impact Imperative: A Space Infrastructure Enabling a Multi-Tiered Earth Defense

Impacting at hypervelocity, an asteroid struck the Earth approximately 65 million years ago in the Yucatan Peninsula a m . This triggered the extinction of almost 70% of the species of life on Earth including the dinosaurs. Other impacts prior to this one have caused even greater extinctions. Preventing collisions with the Earth by hypervelocity asteroids, meteoroids, and comets is the most important immediate space challenge facing human civilization. This is the Impact Imperative. We now believe that while there are about 2000 earth orbit crossing rocks greater than 1 kilometer in diameter, there may be as many as 200,000 or more objects in the 100 m size range. Can anything be done about this fundamental existence question facing our civilization? The answer is a resounding yes! By using an intelligent combination of Earth and space based sensors coupled with an infrastructure of high-energy laser stations and other secondary mitigation options, we can deflect inbound asteroids, meteoroids, and comets and prevent them &om striking the Earth. This can be accomplished by irradiating the surface of an inbound rock with sufficiently intense pulses so that ablation occurs. This ablation acts as a small rocket incrementally changing the shape of the rocks orbit around the Sun. One-kilometer size rocks can be moved sufficiently in about a month while smaller rocks may be moved in a shorter time span. We recommend that space objectives be immediately reprioritized to start us moving quickly towards an infrastructure that will support a multiple option defense capability. Planning and development for a lunar laser facility should be initiated immediately in parallel with other options. All mitigation options are greatly enhanced by robust early warning, detection, and tracking resources to find objects sufficiently prior to Earth orbit passage in time to allow significant intervention. Infrastructure options should include ground, LEO, GEO, Lunar, and libration point laser and sensor stations for providing early warning, tracking, and deflection. Other options should include space interceptors that will carry both laser and nuclear ablators for close range work. Response options must be developed to deal with the consequences of an impact should we move too slowly.

Laser/space material uncooperative propulsion for orbital debris removal and asteroid, meteoroid, and comet deflection

Orbital debris in low-Earth orbit in the size range from 1 to 10 cm in diameter can be detected but not tracked reliably enough to be avoided by spacecraft. It can cause catastrophic damage even to a shielded spacecraft. With adaptive optics, a ground-based pulsed laser ablating the debris surface can produce enough propulsion in several hundred pulses to cause such debris to reenter the atmosphere. A single laser station could remove all of the 1-10 cm debris in three years or less. A technology demonstration of laser space propulsion is proposed which would pave the way for the implementation of such a debris removal system. The cost of the proposed demonstration is comparable with the estimated annual cost of spacecraft operations in the present orbital debris environment. Orbital debris is not the only space junk that is deleterious to the Earth’s environment. Collisions with asteroids have caused major havoc to the Earth’s biosphere many times in the ancient past. Since the possibility still exists f...

Orbital debris removal and meteoroid deflection

Orbital debris in low-Earth orbit in the size range from 1 to 10 cm in diameter can be detected but not tracked reliably enough to be avoided by spacecraft. It can cause catastrophic damage even to a shielded spacecraft. With adaptive optics, a ground-based pulsed laser ablating the debris surface can produce enough propulsion in several hundred pulses to cause such debris to reenter the atmosphere. A single laser station could remove all of the 1 - 10 cm debris in three years or less. A technology demonstration of laser space propulsion is proposed which would pave the way for the implementation of such a debris removal system. The cost of the proposed demonstration is comparable with the estimated annual cost of spacecraft operations in the present orbital debris environment. Orbital debris is not the only space junk that is deleterious to the Earths environment. Collisions with asteroids have caused major havoc to the Earths biosphere many times in the ancient past. Since the possibility still exists for major impacts of asteroids with the Earth, it shown that it is possible to scale up the systems to prevent these catastrophic collisions providing sufficient early warning is available from new generation space telescopes plus deep space radar tracking.

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. We discuss the parallel transport of a vector and the type of closed loop used in the calculation. Our method generalizes similar work of Morganstern, to nonholonomic coordinates and non-Riemannian space-times.

Spinning Fluid Energy-Momentum Tensors in the Einstein-Cartan Theory

A Eulerian variational principle for a perfect fluid in general relativity was presented some years ago.’ Recently we have generalized this variational principle to deal with fluids having intrinsic s p h 2 Recent papers by Bailey and Israel also deal with spinning fluids in general relativity using a different These papers by Bailey and Israel may be consulted for earlier references to this subject. It is thought that the spin of “particles,” protogalaxies, turbulent eddies, or primeval black holes could play an important role in the dynamics of the early universe.’-’ Israel, in a brief study, found a solution for a spinning fluid in an anisotropic (Bianchi I) cosmological model.4 In this example the spin induces a Lense-Thirring rotation of the local inertial axis relative to the directions along the spin of the fluid. Further such studies should be carried out to determine how spin can affect the dynamics of the early universe. The general relativistic energy-momentum tensor for a spinning fluid derived in Reference 2 would be an appropriate starting point for such studies. Our main goal in this paper is to generalize our spinning fluid variational principle of Reference 2 to the Einstein-Cartan (EC) theory. In the EC theory spin takes on an important role as the source of the torsion part of the gravitational field. Thus, what we derive in this paper is a fundamental theory, based on a Lagrangian, which introduces spin into the EC theory for a macroscopic spinning fluid. The torsion-spin equation of our theory leads to the Weyssenhoff convective form for the canonical spin tensor, and the energy-momentum tensor has explicit spin-dependent terms. There have been several recent studies of spinning matter in the EC however, none of these studies deduces the field equations of the theory from a Eulerian variational principle such as in this paper. The theories that we studied in Reference 2 and in this paper are based on the work of Halbwachs, who formulated a Eulerian variational principle for a spinning fluid in special relativity.’ Reference 1 is a generalization of Halbwachs’ theory to general relativity for fluids without intrinsic spin, while Reference 2 is for fluids with intrinsic spin .