# Singularity theorms and perturbation from exact symmetry

• julian
In summary, the singularity theorems can be applied to situations away from exact symmetry, such as the Schwarzschild solution or Friedmann solutions. However, there are currently no accounts addressing the persistence of a 'trapped set' after slight perturbations away from exact symmetry, except for possibly in the book by Hawking and Ellis, which is difficult to read. It may be helpful to read more about the Cauchy problem for GR and the continuous dependency of solutions on initial conditions to determine if trapped surfaces still exist away from exact symmetry. The best place to find information about this may be in Martin Bojowald's book, specifically on page 201 where he mentions that for small perturbations around the Schwarzs
julian
Gold Member
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?

Last edited:
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?

## 1. What is the Singularity Theorem?

The Singularity Theorem is a mathematical concept that states that under certain conditions, the gravitational collapse of a massive object will inevitably result in a singularity, or a point of infinite density and curvature where the laws of physics break down.

## 2. How does the Singularity Theorem relate to the Big Bang theory?

The Singularity Theorem is often used to support the Big Bang theory, as it suggests that the universe began as a singularity and expanded rapidly from there.

## 3. What is perturbation from exact symmetry?

Perturbation from exact symmetry refers to a slight deviation from a perfectly symmetrical system. In physics, this can lead to chaos and unpredictability in the behavior of the system.

## 4. How does perturbation from exact symmetry affect the universe?

In cosmology, perturbation from exact symmetry is believed to be responsible for the formation of structures such as galaxies and clusters of galaxies in the universe. Without this perturbation, the universe would be completely uniform and devoid of any structure.

## 5. Are there any practical applications of studying singularity theorems and perturbation from exact symmetry?

Yes, understanding these concepts can help us better understand the origins and evolution of the universe. It also has practical applications in fields such as astrophysics, where it can help us model and predict the behavior of celestial bodies and systems.

Replies
2
Views
1K
Replies
14
Views
4K
Replies
57
Views
5K
Replies
15
Views
2K
Replies
99
Views
20K
Replies
5
Views
1K
Replies
26
Views
5K
Replies
13
Views
2K
Replies
2
Views
975
Replies
2
Views
2K