What is a sufficient set of restrictions required in order for SCC to hold (if any)?Strong cosmic censorship conjecture (Penrose). Let (##\Sigma_{ab}, h_{ab}, K_{ab}##) be a geodesically complete, asymptotically flat (with ##N## ends), initial data set for the vacuum Einstein equation. Then generically the maximal Cauchy development of this initial data is inextendible... The word ”generically” is included because of known counter-examples...
It seems that you would need the conjecture to be resolved first in order to know if the conditions are sufficient.ergospherical said:In a podcast with Sean Carroll and Roger Penrose (link :) ), it's briefly discussed that one can cook up certain unphysical examples of spacetimes in which SCC is violated. Indeed, in Harvey Reall's BH notes (link), it's written that:
What is a sufficient set of restrictions required in order for SCC to hold (if any)?
May be one should look at this and the following work, where they show that the conjecture is false if one assumes only continuity of the metric. So some differentiability must be a necessary condition. I think it is expected to hold if the metric is in the Sobolev space##W^{1,1}##.ergospherical said:What is a sufficient set of restrictions required in order for SCC to hold (if any)?
"Strong Cosmic Censorship" is a hypothesis proposed by physicist Roger Penrose, which states that in our universe, singularities (points of infinite density) are always hidden behind event horizons and cannot be observed by outside observers.
The sufficient conditions for Strong Cosmic Censorship to hold are the existence of a stable Cauchy horizon and the validity of the cosmic censorship conjecture, which states that singularities must be hidden from outside observers by an event horizon.
The conditions for Strong Cosmic Censorship are based on the laws of general relativity, which describe the behavior of gravity in our universe. These conditions ensure that the laws of general relativity hold and that singularities are always hidden from outside observers.
The Strong Cosmic Censorship hypothesis is significant because it helps to maintain the predictability and stability of our universe. If singularities were observable, it would lead to violations of the laws of physics and make the universe unpredictable.
There are ongoing debates and research in the scientific community about the validity of Strong Cosmic Censorship. Some theories, such as the "cosmic no-hair conjecture," support the hypothesis, while others, such as the "cosmic censorship theorem," suggest that it may not always hold. Currently, there is no conclusive evidence either supporting or refuting Strong Cosmic Censorship.