Geodesic deviation equation inf(T)gravity

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

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...

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...

The String Deviation Equation

It is well known that the relative motion of many particles can be described by the geodesic deviation equation. Less well known is that the geodesic deviation equation can be derived from the second covariant variation of the point particle’s action. Here it is shown that the second covariant variation of the string action leads to a string deviation equation. This equation is a candidate for ...