Operational significance of the deviation equation in relativistic geodesy

Deviation equation: Second order differential equation for the 4-vector which measures the distance between reference points on neighboring world lines in spacetime manifolds. Relativistic geodesy: Science representing the Earth (or any planet), including the measurement of its gravitational field, in a four-dimensional curved spacetime using differential-geometric methods in the framework of Einstein's theory of gravitation (General Relativity).Comment: 9 pages, 4 figures, contribution to the "Encyclopedia of Geodesy". arXiv admin note: text overlap with arXiv:1811.1047

A Snapshot of J. L. Synge

A brief description is given of the life and influence on relativity theory of Professor J. L. Synge accompanied by some technical examples to illustrate his style of work

Numerical Calculation of Diffraction Coefficients in Anisotropic Media

Ultrasonic inspection is used to detect and size crack-like defects in pressure vessels and pipework used in the nuclear industry. Reliable inspection can only be achieved if the inspection technique is understood, is optimised and subsequently applied correctly. Austenitic steels are used because of their corrosion resistance and toughness. Welds and centrifugally cast materials tend to crystallise with grains larger than the ultrasonic wavelength required to achieve the desired resolution in the inspection and thus appear anisotropic. Since the grains in a weld grow along the, varying, directions of maximum heat flux during cooling, the welds are inhomogeneous as well as anisotropic. We wish to understand the ultrasonic signals scattered by cracks in such inhomogeneous anisotropic materials. To calculate large numbers of cases we would like to use a relatively efficient tool: (ray tracing) and wish to incorporate the diffraction and reflection which occurs at the defect through the use of diffraction or scattering coefficients.</p

The Hypothesis of Locality and its Limitations

The hypothesis of locality, its origin and consequences are discussed. This supposition is necessary for establishing the local spacetime frame of accelerated observers; in this connection, the measurement of length in a rotating system is considered in detail. Various limitations of the hypothesis of locality are examined.Comment: LaTeX file, no figures, 14 pages, to appear in: "Relativity in Rotating Frames", edited by G. Rizzi and M.L. Ruggiero (Kluwer Academic Publishers, Dordrecht, 2003

Elastic Wave Diffraction at Cracks in Anisotropic Materials

Ultrasonic inspection is used to confirm that there are no defects of concern in various regions of a nuclear reactor primary circuit. All materials are naturally anisotropic, but if the grains are small relative to the ultrasonic wavelength and are also randomly oriented, then the material will appear as homogeneous and isotropic as in ferritic steel. The ultrasonic wavelength is chosen as a compromise between resolution of defect size and acoustic noise from grain boundaries. In austenitic steel, the wavelength chosen will typically be smaller than the grain size, at least in one direction. The grains are not randomly oriented but exhibit macroscopic patterns which depend on the welding process, and the material is neither homogeneous nor isotropic

Isotropy of the velocity of light and the Sagnac effect

In this paper, it is shown, using a geometrical approach, the isotropy of the velocity of light measured in a rotating frame in Minkowski space-time, and it is verified that this result is compatible with the Sagnac effect. Furthermore, we find that this problem can be reduced to the solution of geodesic triangles in a Minkowskian cylinder. A relationship between the problems established on the cylinder and on the Minkowskian plane is obtained through a local isometry.Comment: LaTeX, 13 pages, 3 eps figures; typos corrected, added references, minor changes; to appear in "Relativity in Rotating Frames", ed. G. Rizzi G. and M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht (2003

Measuring the gravitational field in General Relativity: From deviation equations and the gravitational compass to relativistic clock gradiometry

How does one measure the gravitational field? We give explicit answers to this fundamental question and show how all components of the curvature tensor, which represents the gravitational field in Einstein's theory of General Relativity, can be obtained by means of two different methods. The first method relies on the measuring the accelerations of a suitably prepared set of test bodies relative to the observer. The second methods utilizes a set of suitably prepared clocks. The methods discussed here form the basis of relativistic (clock) gradiometry and are of direct operational relevance for applications in geodesy.Comment: To appear in "Relativistic Geodesy: Foundations and Application", D. Puetzfeld et. al. (eds.), Fundamental Theories of Physics, Springer 2018, 52 pages, in print. arXiv admin note: text overlap with arXiv:1804.11106, arXiv:1511.08465, arXiv:1805.1067

Higher Dimensional Cylindrical or Kasner Type Electrovacuum Solutions

We consider a D dimensional Kasner type diagonal spacetime where metric functions depend only on a single coordinate and electromagnetic field shares the symmetries of spacetime. These solutions can describe static cylindrical or cosmological Einstein-Maxwell vacuum spacetimes. We mainly focus on electrovacuum solutions and four different types of solutions are obtained in which one of them has no four dimensional counterpart. We also consider the properties of the general solution corresponding to the exterior field of a charged line mass and discuss its several properties. Although it resembles the same form with four dimensional one, there is a difference on the range of the solutions for fixed signs of the parameters. General magnetic field vacuum solution are also briefly discussed, which reduces to Bonnor-Melvin magnetic universe for a special choice of the parameters. The Kasner forms of the general solution are also presented for the cylindrical or cosmological cases.Comment: 16 pages, Revtex. Text and references are extended, Published versio

General Relativistic Gravity Gradiometry

Gravity gradiometry within the framework of the general theory of relativity involves the measurement of the elements of the relativistic tidal matrix, which is theoretically obtained via the projection of the spacetime curvature tensor upon the nonrotating orthonormal tetrad frame of a geodesic observer. The behavior of the measured components of the curvature tensor under Lorentz boosts is briefly described in connection with the existence of certain special tidal directions. Relativistic gravity gradiometry in the exterior gravitational field of a rotating mass is discussed and a gravitomagnetic beat effect along an inclined spherical geodesic orbit is elucidated.Comment: 18 pages, invited contribution to appear in "Relativistic Geodesy: Foundations and Applications", D. Puetzfeld et al. (eds.), 2018; v2: matches version published in: D. Puetzfeld and C. L\"ammerzahl (eds.) "Relativistic Geodesy" (Springer, Cham, 2019), pp. 143-15

The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org