# Geodesic deviation in 2d

1. May 6, 2015

### AcidRainLiTE

In 2 dimensions, is the geodesic deviation equation governed by a single scalar, independent of the direction of the geodesics? That is, if ξ is the separation of two nearby geodesics, do we have $$d^2 \xi/ds^2 + R\xi = 0$$ where R is a scalar that is completely independent of the direction of the geodesics?

If so, how can we see that there can be no directional dependence in 2d?

2. May 7, 2015

### Mentz114

By 2D do you mean $t,x$ ? So if you have a metric $ds^2=-g_{00} dt^2 + g_{11}dx^2$, can you work it out explicitly ? If the velocities of the geodesics depend on $t$ or $x$, is that directional dependence ?

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