Measuring the Gravitational Field in General Relativity: From Deviation Equations and the Gravitational Compass to Relativistic Clock Gradiometry

Abstract

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. *

Measurement of Gravitational Coupling between Millimeter-Sized Masses

“…We also note that our method allowed us to directly measure the position-dependence of the gravitational force, which constitutes a 1D-mapping of the gravitational field strength. A more complex test mass geometry may enable a full mapping of the metric tensor of such small source masses 49,50 . Our experiment provides a viable path to enter and explore a new regime of gravitational physics that involves precision tests of gravity with isolated microscopic source masses at or below the Planck mass.…”

Gravitational clock compass and the detection of gravitational waves

“…In this work we presented an alternative derivation of the gravitational clock compass, previously proposed in [8][9][10], by means of the approximation technique developed in [14][15][16]. We were able to specialize the general compass setup to two special types of space-times, describing plane gravitational waves and waves moving radially to an observer.…”

“…Building upon a preceding series of works [8][9][10] -in which we derived general prescriptions for the setup of the constituents of a device called a "gravitational compass" [11] and a "clock compass", i.e. realizations of gradiometers in the context of the theory of General Relativity -we are now going to study how clocks can be used in an operational way to explicitly map gravitational wave space-times by means of mutual frequency comparisons.…”

Extended gravitational clock compass: new exact solutions and simulations

“…In particular, we will study how the precision of the determination of the physical parameters depends on the distance of the clocks to the reference world line Y . We start by labeling 9 different initial values for the positions of the clocks, as follows: (1) (5) (6)…”

“…Here we make use of clock measurements in order to determine the curvature of spacetime. This method has been developed in [1,5] and can be viewed as complementary to the use of deviation equations [6] and swarms of test bodies. An alternative derivation of the clock compass and its use in the context of exact gravitational wave spacetimes can be found in [7].…”