**Subject:** Lemaitre / Tolman / Bondi Metric

**Date:** Sat, 31 May 2008 12:18:25 EDT

This describes a spherically symmetric cloud of dust alleged to be expanding or collapsing under gravitation. It is an exact solution of the Einstein field equation found by Lemaitre in 1933, Tolman in 1934 and Bondi in 1947:

ds squared = c squared dt squared – A dr squared – R squared d cap omega squared

where

A = (R’) squared / (1 – 2E)

with

R = R(t, r), R’ = partial R / partial r, E = E(r)

We already know that the Friedmann Lemaitre Robertson Walker metric failed the dual identity test, so this one will fail also. The Maxima code will work out all the functional derivatives needed.