Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

Rotating, charged, and uniformly accelerating mass in general relativity

On 21 July 1969, during the first manned lunar mission, Apollo 11, the first retroreflector array was placed on the moon, enabling highly accurate measurements of the Earthmoon separation by means of laser ranging. Lunar laser ranging (LLR) turns the Earthmoon system into a laboratory for a broad range of investigations, including astronomy, lunar science, gravitational physics, geodesy, and geodynamics. Contributions from LLR include the three-orders-of-magnitude improvement in accuracy in the lunar ephemeris, a several-orders-of-magnitude improvement in the measurement of the variations in the moon's rotation, and the verification of the principle of equivalence for massive bodies with unprecedented accuracy. Lunar laser ranging analysis has provided measurements of the Earth's precession, the moon's tidal acceleration, and lunar rotational dissipation. These scientific results, current technological developments, and prospects for the future are discussed here.

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Lunar Laser Ranging: A Continuing Legacy of the Apollo Program

The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work. This paper discusses the conceptual basis, founded on special and general relativity, for navigation using GPS. Relativistic principles and effects which must be considered include the constancy of the speed of light, the equivalence principle, the Sagnac effect, time dilation, gravitational frequency shifts, and relativity of synchronization. Experimental tests of relativity obtained with a GPS receiver aboard the TOPEX/POSEIDON satellite will be discussed. Recently frequency jumps arising from satellite orbit adjustments have been identified as relativistic effects. These will be explained and some interesting applications of GPS will be discussed.

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Relativity in the Global Positioning System

Material properties emerge from phenomena on scales ranging from Angstroms to millimeters, and only a multiscale treatment can provide a complete understanding. Materials researchers must therefore understand fundamental concepts and techniques from different fields, and these are presented in a comprehensive and integrated fashion for the first time in this book. Incorporating continuum mechanics, quantum mechanics, statistical mechanics, atomistic simulations and multiscale techniques, the book explains many of the key theoretical ideas behind multiscale modeling. Classical topics are blended with new techniques to demonstrate the connections between different fields and highlight current research trends. Example applications drawn from modern research on the thermo-mechanical properties of crystalline solids are used as a unifying focus throughout the text. Together with its companion book, Continuum Mechanics and Thermodynamics (Cambridge University Press, 2011), this work presents the complete fundamentals of materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.

Modeling Materials: Continuum, Atomistic and Multiscale Techniques

Geodesy is devoted to the determination of the shape, size, and gravity field of the Earth. Its methods include triangulation, leveling, gravity surveys, and tracking by artificial satellites. The results of its observations typically hold for time periods varying from a few hours to decades. In contrast, in geophysics (seismology in particular) one deals with very short periods of an hour or less, while in geological processes, one frequently considers periods of a million years or more. In Lambeck's book, the author treats the middle ground between these two geophysical extremes, which is concerned with the slow deformation of the Earth. He quite appropriately calls this geophysical geodesy, and its topics include crustal motion, spatial and temporal variation of the gravity field, rotation, and tidal deformations of the Earth. Hence geophysical geodesy aims to bridge a traditional gap between geodesy and geophysics.

Geophysical Geodesy: The Slow Deformation of the Earth

Foundations of differential geodesy

The Lanczos tensor is studied by using the van der Waerden two component spinor calculus. The algebraic and invariant theory of the resulting Lanczos spinor is investigated, and the spinor form of the equation relating the Lanczos and Weyl tensor is derived. The Weyl-Lanczos equations are transcribed into spin coefficient form and the radial dependence of the Lanczos coefficients is determined for eight relativistic space-times.

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The theory of the Lanczos spinor

On etudie les applications conformes entre une paire d'espaces de Riemann a 2 et 3 dimensions. On considere les equations de Cauchy-Riemann a deux dimensions et on montre qu'elles peuvent se deduire de conditions geometriques. On deduit les equations de Cauchy-Riemann generalisees pour des surfaces courbes

Joseph D. Zund

Papers

Geophysical Geodesy: The Slow Deformation of the Earth

Foundations of differential geodesy

The theory of the Lanczos spinor

The tensorial form of the Cauchy-Riemann equations

George David Birkhoff and John von Neumann: A Question of Priority and the Ergodic Theorems, 1931–1932