# Lemaitre Coordinate from the E-F coordinate

1. May 6, 2012

### johnahn

How can Eddington-Finkelstein coordinate be transformed into Lemaitre coordinate?

I know the transformation between the Lemaitre and Schwarzschild coordinate, and also between Eddington-Finkelstein and Schwarzschild coordinate.

So I tried to find the connection between Lemaitre and E-F coordinate from that, but it is very complicated..

Can you give me the explicit formula for that?

2. May 6, 2012

### Mentz114

If L1 takes LeMaitre basis to the Schwarzschild coordinate basis and L2 takes SS to E.F., then does L1L2 not take LeMaitre to EF basis ?

Formally, if μ is the Schwarzschild coordinate index, a is a LeMaitre frame index and A is an EF frame index then
\begin{align} v^\mu &= \Lambda^\mu_a v^a\\ v^A &= \Lambda^A_\mu v^\mu = \Lambda^A_\mu(\Lambda^\mu_a v^a) = (\Lambda^A_\mu\Lambda^\mu_a)v^a \end{align}

Last edited: May 6, 2012