# Acceleration in a new Coordinate System - General Relativity

1. Oct 20, 2016

### kent davidge

1. The problem statement, all variables and given/known data

Below: Jac = Jacobian matrix; ξ = d/dφ for some continuous parameter φ which labels different points on the worldline.

(I'm sorry for my poor English.)
Consider a new coordinate system xµ' which differs from the original Cartesian coordinate system xµ; the Cartesian coordinates xµ can be written as a function of these new coordinates xµ = xµ (xµ'). Show that the equation of motion can be written in these new xµ' coordinates as ξ²xµ' + Γµ'ν'λ'ξxν'ξxλ' = 0 for some Γµ'ν'λ' which you must compute; Γµ'ν'λ' is known as the Christoffel symbol. These extra Christoffel terms in the equation of motion can be thought of as ”fictitous forces” that arise in an accelerated reference frame.

2. Relevant equations

xµ' = Jac * xµ

3. The attempt at a solution

I've tried to solve this by deriving xµ' with respect to φ using the chain rule, but that did not work. Unfortunately I could not put my work here, but it was just what I said: I've used the chain rule to derive xµ' with respect to φ.

2. Oct 26, 2016