Related papers: General Relativity and Geodesy
One of geodesy's main tasks is to determine the gravity field of the Earth. High precision clocks have the potential to provide a new tool in a global determination of the Earth's gravitational potential based on the gravitational redshift.…
The Earth's geoid is one of the most essential and fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to…
Time measured by an ideal clock crucially depends on the gravitational potential and velocity of the clock according to general relativity. Technological advances in manufacturing high-precision atomic clocks have rapidly improved their…
In section 2, we introduce fundamental concepts of GR concerning the measurement of time, relativistic reference systems and we review the recent literature of chronometric geodesy. In section 3 we introduce the theory of frequency standard…
General Relativity (GR) is shown to be a complete theory with respect to the isochrony of the pendulum. This guarantees that time can be measured with a mechanical clock within the theory itself as a matter of principle. The proper and…
Recent developments in fundamental physics (in theory as well as in technology) provide novel capabilities for geodetic applications such as refined observations of the Earth`s gravity field. We will focus on two new concepts: one applies…
We show how a suitably prepared set of clocks can be used to determine all components of the gravitational field in General Relativity. We call such an experimental setup a clock compass, in analogy to the usual gravitational compass.…
We discuss theoretical formalisms concerning with experimental verification of General Relativity (GR). Non-metric generalizations of GR are considered and a system of postulates is formulated for metric-affine and Finsler gravitational…
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…
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,…
Several satellite missions, devoted to the study of the Earth gravity field, have been launched (like CHAMP, recently). This year, GRACE (Gravity Recovery and Climate Experiment) will allow us to obtain a more precise geoid. But the most…
Geodesy in a Newtonian framework is based on the Newtonian gravitational potential. The general-relativistic gravitational field, however, is not fully determined by a single potential. The vacuum field around a stationary source can be…
The geoid is the true physical figure of the Earth, a particular equipotential surface of the gravity field of the Earth that accounts for the effect of all subsurface density variations. Its shape approximates best (in the sense of least…
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…
The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability and uncertainty, are already being used to test physical theories and herald a…
Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
Due to the accuracy now reached by space geodetic techniques, and also considering some modelisations, the temporal variations of some Earth Gravity Field coefficients can be determined. They are due to Earth oceanic and solid tides, as…
The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of…
We develop, in the context of general relativity, the notion of a geoid -- a surface of constant "gravitational potential". In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general…