Sufficient Conditions for Strong Cosmic Censorship

[ergospherical]

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:

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...

What is a sufficient set of restrictions required in order for SCC to hold (if any)?

 

[martinbn]

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)?

It seems that you would need the conjecture to be resolved first in order to know if the conditions are sufficient.

 

[martinbn]

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$W^{1,1}$.

 

[romsofia]

https://arxiv.org/pdf/1505.06390.pdf

Section 4/5 may be what you're looking for, but the paper gives a good historical perspective as well.

 

[ergospherical]

A recent lecture by Prof Harvey Reall on our present understanding of SCC:

Harvey Reall - Some recent developments in strong cosmic censorship