We present a definition of the geoid that is based on the formalism of general relativity without approximations; i.e. it allows for arbitrarily strong gravitational fields. For this reason, it applies not only to the Earth and other planets but also to compact objects such as neutron stars. We define the geoid as a level surface of a time-independent redshift potential. Such a redshift potential exists in any stationary spacetime. Therefore, our geoid is well defined for any rigidly rotating object with constant angular velocity and a fixed rotation axis that is not subject to external forces. Our definition is operational because the level surfaces of a redshift potential can be realized with the help of standard clocks, which may be connected by optical fibers. Therefore, these surfaces are also called "isochronometric surfaces." We deliberately base our definition of a relativistic geoid on the use of clocks since we believe that clock geodesy offers the best methods for probing gravitational fields with highest precision in the future. However, we also point out that our definition of the geoid is mathematically equivalent to a definition in terms of an acceleration potential, i.e. that our geoid may also be viewed as a level surface orthogonal to plumb lines. Moreover, we demonstrate that our definition reduces to the known Newtonian and post-Newtonian notions in the appropriate limits. As an illustration, we determine the isochronometric surfaces for rotating observers in axisymmetric static and axisymmetric stationary solutions to Einstein's vacuum field equation, with the Schwarzschild metric, the Erez-Rosen metric, the q-metric and the Kerr metric as particular examples.

Over almost five decades of development and improvement, Magnetic Resonance Imaging (MRI) has become a rich and powerful, non-invasive technique in medical imaging, yet not reaching its physical limits. Technical and physiological restrictions constrain physically feasible developments. A common solution to improve imaging speed and resolution is to use higher field strengths, which also has subtle and potentially harmful implications. However, patient safety is to be considered utterly important at all stages of research and clinical routine. Here we show that dynamic metamaterials are a promising solution to expand the potential of MRI and to overcome some limitations. A thin, smart, non-linear metamaterial is presented that enhances the imaging performance and increases the signal-to-noise ratio in 3T MRI significantly (up to eightfold), whilst the transmit field is not affected due to self-detuning and, thus, patient safety is also assured. This self-detuning works without introducing any additional overhead related to MRI-compatible electronic control components or active (de-)tuning mechanisms. The design paradigm, simulation results, on-bench characterization, and MRI experiments using homogeneous and structural phantoms are described. The suggested single-layer metasurface paves the way for conformal and patient-specific manufacturing, which was not possible before due to typically bulky and rigid metamaterial structures.

For metrology, geodesy and gravimetry in space, satellite based instruments and measurement techniques are used and the orbits of the satellites as well as possible deviations between nearby ones are of central interest. The measurement of this deviation itself gives insight into the underlying structure of the spacetime geometry, which is curved and therefore described by the theory of general relativity (GR). In the context of GR, the deviation of nearby geodesics can be described by the Jacobi equation that is a result of linearizing the geodesic equation around a known reference geodesic with respect to the deviation vector and the relative velocity. We review the derivation of this Jacobi equation and restrict ourselves to the simple case of the spacetime outside a spherically symmetric mass distribution and circular reference geodesics to find solutions by projecting the Jacobi equation on a parallel propagated tetrad as done by Fuchs. Using his results, we construct solutions of the Jacobi equation for different physical initial scenarios inspired by satellite gravimetry missions and give a set of parameter together with their precise impact on satellite orbit deviation. We further consider the Newtonian analog and construct the full solution, that exhibits a similar structure, within this theory.Comment: 6 pages, 3 figures, contribution to conference on Metrology for Aerospace 2015 - relativistic metrology sessio

In a previous paper, we have considered the Regge-Wheeler equation for fields of spin s = 0, 1 or 2 on the Schwarzschild spacetime in coordinates that are regular at the horizon. In particular, we have constructed in Eddington-Finkelstein (EF) coordinates exact solutions in terms of series that are regular at the horizon and converge on the entire open domain from the central singularity to infinity. Here, we extend this earlier work in two different directions. First, we consider in EF coordinates a massive scalar field that can serve as a dark matter candidate. Second, we extend the treatment of the massless case to Painlevé-Gullstrand (PG) coordinates, which are associated with radially infalling observers. Int. J. Mod. Phys. D 2015.24. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/12/15. For personal use only.