Geodesic deviation equation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e26" altimg="si5.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>-gravity

Epicyclic orbital oscillations in Newton’s and Einstein’s gravity from the geodesic deviation equation

In a recent paper Abramowicz and Kluźniak [1] have discussed the problem of epicyclic oscillations in Newton’s and Einstein’s dynamics and have shown that Newton’s dynamics in a properly curved three-dimensional space is identical to testbody dynamics in the three-dimensional optical geometry of Schwarzschild spacetime. One of the main results of this paper was the proof that different behaviou...

Geodesic Deviation of Photons in Einstein and Higher Derivative Gravity

We derive the wave equation obeyed by electromagnetic fields in curved spacetime. We find that there are Riemann and Ricci curvature coupling terms to the photon polarisation which result in a polarisation dependent deviation of the photon trajectories from null geodesics. Photons are found to have an effective mass in an external gravitational field and their velocity in an inertial frame is i...

The Quantization of Geodesic Deviation

There exists a two parameter action, the variation of which produces both the geodesic equation and the geodesic deviation equation. In this paper it is shown that this action can be quantized by the canonical method, resulting in equations which generalize the Klein-Gordon equation. The resulting equations might have applications, and also show that entirely unexpected systems can be quantized...

Geodesic Deviation and Weak-Field Solutions

The Geodesic Equation

What does it mean to be straight? That the direction of the line does not change. In other words, the unit tangent vector to the curve remains constant. Note that the speed does not need to be constant; only the direction remains the same. However, if we are only interested in the shape of the line, and not in the particular manner in which we move along it, it is convenient to use a descriptio...