The discussion revolves around the strong cosmic censorship (SCC) conjecture in the context of general relativity, exploring the conditions under which SCC may hold or be violated. Participants reference various sources, including podcasts and academic papers, to examine the theoretical implications and necessary restrictions related to SCC.
Participants express uncertainty regarding the sufficient conditions for SCC, with multiple competing views on what those conditions might entail. The discussion remains unresolved.
Some limitations include the dependence on specific definitions of differentiability and continuity, as well as the unresolved status of the SCC conjecture itself.
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)?