Singularity theorms and perturbation from exact symmetry

[julian]

The singularity theorems apply to situations away from exact symmetry ... away from Schwarzschild solution or Friedmann solutions for example. There are a number of accounts of the singularity theorems but none addressing the problem of proving a 'trapped set' still persists after slight perturbation away from exact symmetry (except maybe Hayking and Ellis? Difficult book to read.).

Should I read more about the Cauchy problem for GR and on how solutions depend continuously on the initial conditions to find out if trapped surfaces still exist away from exact symmetry?

Where's the best place to find out about this stuff?

 

[julian]

In martin Bojowald's book's ,page 201 he says "even if one perturbs around the Schwarzschild solution, specific values of expansions of null congruemces may change, but for sufficiently small perturbations they will remain negative if they are negative for the unpereturbed solution"

Does anyone know a place to look to find the proof of this?