Singularity theorms and perturbation from exact symmetry

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SUMMARY

The discussion centers on the singularity theorems in general relativity (GR) and their applicability to scenarios deviating from exact symmetry, specifically referencing the Schwarzschild and Friedmann solutions. Participants highlight the challenge of proving the persistence of 'trapped sets' after slight perturbations from symmetry, with mentions of Hayking and Ellis as potential sources. Martin Bojowald's work is cited, indicating that small perturbations around the Schwarzschild solution can maintain negative expansions of null congruences. The conversation emphasizes the need for further exploration of the Cauchy problem in GR to understand the continuity of solutions and the existence of trapped surfaces.

PREREQUISITES
  • Understanding of general relativity (GR) principles
  • Familiarity with singularity theorems
  • Knowledge of the Cauchy problem in GR
  • Basic concepts of perturbation theory in physics
NEXT STEPS
  • Study Martin Bojowald's book, focusing on page 201 for insights on perturbations around the Schwarzschild solution
  • Research the Cauchy problem in general relativity to grasp the dependence of solutions on initial conditions
  • Investigate the implications of trapped surfaces in perturbed spacetime geometries
  • Explore literature on Hayking and Ellis for advanced discussions on singularity theorems
USEFUL FOR

Researchers, physicists, and students in theoretical physics, particularly those focusing on general relativity, singularity theorems, and perturbation theory.

julian
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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?
 
Last edited:
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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?
 

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