Theoretical Tools for Relativistic Gravimetry, Gradiometry and Chronometric Geodesy and Application to a Parameterized Post-Newtonian Metric

Delva, Pacôme; Geršl, Jan

doi:10.3390/universe3010024

Cited by 8 publications

(8 citation statements)

References 69 publications

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“…The equation of geodesic deviation [Eqs. (35.14) and (35.15) of MTW [31]] in the proper reference frame [48] describes the oscillations of locations of test particles which are induced by the wave as measured by an observer in the spatial origin of the proper reference frame. The equation is often solved in a convenient transverse-traceless (T T ) gauge where h T T jk = 2ω −2 R j0k0 (Box 35.1 in MTW [31]).…”

Section: The Case Of ≥ 2 Small Values Of Rmentioning

confidence: 99%

Visualizing gravitational Bessel waves

et al. 2019

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We explicitly derive a vortex inspired solution for the metric perturbation within the linearized Einsteins general theory of relativity in arbitrary dimensions D ≥ 4. We focus on D = 4 where our solution is the gravitational analog of the well-known electromagnetic (or electron) Bessel vortex beams. Next we visualize the perturbed spacetime via tidal tendexes and frame-drag vortexes. We display and analyze mostly two-dimensional sections of the tendexes and the vortexes for different values of an angular momentum of the wave solution. Corresponding geodesic deviation equations are solved and the results are visualized. We show that the physically most important quadrupolelike case leads to a wave with rotating polarization. We discuss asymptotical features of the found solution. We provide also several 3D plots of tendex lines. One of them concerns a special cylindricallike case and we utilize the topological classification of singularities of the depicted line fields as an approach to characterize the radiation field.

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Section: The Case Of ≥ 2 Small Values Of Rmentioning

confidence: 99%

Visualizing gravitational Bessel waves

et al. 2019

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“…[11] and [12]. Reference [13] contains a comprehensive summary of theoretical methods in relativistic gravimetry, chronometric geodesy, and related fields as well as applications to a parametrized post-Newtonian metric. Our notational conventions and a list of symbols can be found in Appendix B.…”

Section: Introductionmentioning

confidence: 99%

Definition of the relativistic geoid in terms of isochronometric surfaces

et al. 2017

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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.

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“…In order to analyze gravitational effects in quantum optics experiments in a laboratory environment, we must prescribe the metric local to a laboratory observer, which can be done in the so-called proper reference frame -a reference frame naturally adapted to an arbitrary observer in curved space-time. We follow references [1,41] in the construction of the proper reference frame and its relation to the background PN frame, by providing key equations and brief explanations, whilst leaving explicit details to the references therein.…”

Section: B the Metricmentioning

confidence: 99%

“…Therefore, for a free-falling (parallel-transported) observer, such quantities vanish entirely. Then, the first non-trivial components in the metric are at O x 2 and depend on Reimann curvature [41] (see also Ch. 13 of [1]).…”

Section: Proper Reference Frame: the Local Metricmentioning

confidence: 99%

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Relativistic frame-dragging and the Hong-Ou-Mandel dip $-$ a primitive to gravitational effects in multi-photon quantum-interference

Brady,

Haldar

2020

Preprint

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We investigate the Hong-Ou-Mandel (HOM) effect -a two-photon quantum-interference effectin the space-time of a rotating spherical mass. In particular, we analyze a common-path HOM setup restricted to the surface of the earth and show that, in principle, general-relativistic frame-dragging induces observable shifts in the HOM dip. For completeness and correspondence with current literature, we also analyze the emergence of gravitational time-dilation effects in HOM interference, for a dual-arm configuration. The formalism thus presented establishes a basis for encoding generalrelativistic effects into local, multi-photon, quantum-interference experiments. Demonstration of these instances would signify genuine observations of quantum and general relativistic effects, in tandem, and would also extend the domain of validity of general relativity, to the arena of quantized electromagnetic fields.

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Theoretical Tools for Relativistic Gravimetry, Gradiometry and Chronometric Geodesy and Application to a Parameterized Post-Newtonian Metric

Cited by 8 publications

References 69 publications

Visualizing gravitational Bessel waves

Visualizing gravitational Bessel waves

Definition of the relativistic geoid in terms of isochronometric surfaces

Relativistic frame-dragging and the Hong-Ou-Mandel dip $-$ a primitive to gravitational effects in multi-photon quantum-interference

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