# On the singularity $r=0$ of the Schwarzschild metric

I faced following sentences:

Unlike the co-ordinate singularity at $r = 2M$, the origin of the Schwarzschild metric $r = 0$ has a true curvature singularity. It was first believed that this singularity was an artifact of spherical symmetry and that a generic collapse would evade the singularity. However, work by Hawking and Penrose showed that this was not so and that singularities were generic rather than special. The ubiquity of singularities is guaranteed by the singularity theorems by Hawking and Penrose.

Question1: What is the meaning of "generic collapse"?

Question2: When is a singularity an artifact of spherical symmetry?

• I believe most of your questions (if not all - also those in the comments following Danu's reply) are covered in Gen. Rel. Grav. 34 (2002), 1141-1165, also (freely) available here.
– user34134
Nov 28, 2013 at 20:15

I believe that both questions are easily answered even without a GR background. Saying that something is an artifact of spherical symmetry means, in this context, that it was expected that the singularity would not occur in cases where no perfect symmetry is assumed. Since perfect spherical symmetry only ever occurs in theory, this would solve the problem of the singularity: it would never appear in practice. The real-life case is referred to as 'generic', denoting pretty much that it does not have any special properties (like perfect spherical symmetry) associated with it.

• Thanks for the answer. If you are right, then how does a generic collapse evade the singularity? I think that generic collapse makes singularity and can't evade it. Can you explain me? Nov 28, 2013 at 18:43
• @Bakhoda: it doesn't evade it, as the paragraph you've quoted says. Some people hoped that singularities only occur in cases of perfect symmetry, but Hawking and Penrose showed that those people were mistaken. Nov 28, 2013 at 18:47
• It doesn't, that's the whole point! It was only thought it might, because a singularity seemed strange/unnatural.
– Danu
Nov 28, 2013 at 18:47
• I know that it doesn't in real life. My question is that why did people believe that a generic collapse can evade the singularity? Nov 28, 2013 at 18:54
• @Bakhoda: afaik, there was no exact argument except hope by analogy with Newtonian gravitation. In the Newtonian case, perfectly spherical collapse introduces a singularity, but result this is unstable and imperfections in the symmetry avoid the singularity. So I think some people hoped a similar thing would happen in GTR. Nov 28, 2013 at 19:01

In addition to Danu's answer, it is worth mentioning that there is another class of solutions in GR which arise as the artifacts of special symmetry: naked sigularities (that is, singularities without event horizons).

The cosmic censorship hypothesis states that for a 'reasonable' matter, dynamical evolution from generic initial conditions can never produce a naked singularity.

Nevertheless, there exist solutions in which the collapse of matter results in the formation of naked singularities. It's just the initial conditions for such solutions are 'special', often possessing high degree of symmetry (such as spherical symmetry), and thus would likely could not be realized in reality.

Interestingly, the existence of such naked singularities was the subject of a bet between S. Hawking and J. Preskill/K. Thorne. Hawking conceded the original version of the bet "on technicalities" accepting that naked singularities can form under very special "nongeneric" conditions, and proposed a new version, which is still open.