Coupled inertial and gravitational effects in the proper reference frame of an accelerated, rotating observer

Abstract

To the second order in metric and the first order in equations of motion in the local coordinates of an accelerated rotating observer, the inertial effects and gravitational effects are simply additive. To look into the coupled inertial and gravitational effects, we derive the third-order expansion of the metric and the second-order expansion of the equations of motion in local coordinates. Besides purely gravitational (purely curvature) effects, the equations of motion contain, in this order, the following coupled inertial and gravitational effects: redshift corrections to electric, magnetic, and double-magnetic type curvature forces; velocity-induced special relativistic corrections; and electric, magnetic, and double-magnetic type coupled inertial and gravitational forces. An example is provided with a static observer in the Schwarzchild spacetime.

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

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Rigid covariance, equivalence principle and Fermi rigid coordinates: gravitational waves

“…They studied accelerated reference systems with rotation. Li and Ni in [15,16], Nesterov [17], Marzlin [18], have all made contributions in the same direction, calculating increasing approximation orders of the metric using FNC. In the present work, our focus is on the way FNC are constructed.…”

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

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