The ``close limit,'' a method based on perturbations of Schwarzschild
spacetime, has proved to be a very useful tool for finding approximate
solutions to models of black hole collisions. Calculations carried out with
second order perturbation theory have been shown to give the limits of
applicability of the method without the need for comparison with numerical
relativity results. Those second order calculations have been carried out in a
fixed coordinate gauge, a method that entails conceptual and computational
difficulties. Here we demonstrate a gauge invariant approach to such
calculations. For a specific set of models (requiring head on collisions and
quadrupole dominance of both the first and second order perturbations), we give
a self contained gauge invariant formalism. Specifically, we give (i) wave
equations and sources for first and second order gauge invariant wave
functions; (ii) the prescription for finding Cauchy data for those equations
from initial values of the first and second fundamental forms on an initial
hypersurface; (iii) the formula for computing the gravitational wave power from
the evolved first and second order wave functions.Comment: 18 pages, no figure
