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However, a completely different situation could possibly exist during the collapse leading to the formation of an astrophysical black hole. During the collapse, there is infalling matter present, so the Ricci tensor need not vanish. Indeed, it appears that in models of gravitational collapse, the singularity, during the period of collapse, is a timelike (locally naked) singularity (Joshi), meaning that it is completely different in character from the spacelike singularity of an eternal black hole such as a Schwarzschild black hole. It appears that in such calculations, the density of matter does blow up at the singularity, which suggests that it may be an s.c.s. during formation.

When we think about a black hole, we usually imagine by default the kind of eternal black hole describe by the Schwarzschild spacetime. Some significant difficulties occur even in this simplest possible case. As noted above, the singularity may have a completely different character than the singularity occurring during the gravitational collapse of an astrophysical black hole, and this leads to suspicion that by considering the Schwarzschild case, we are omitting essential considerations.

However, a completely different situation could possibly exist during the collapse leading to the formation of an astrophysical black hole. During the collapse, there is infalling matter present, so the Ricci tensor need not vanish. Indeed, it appears that in some fairly realistic models of gravitational collapse, the singularity, during the period of collapse, is a timelike (locally naked) singularity (Joshi), meaning that it is completely different in character from the spacelike singularity of an eternal black hole such as a Schwarzschild black hole. It appears that in such calculations, the density of matter does blow up at the singularity, which suggests that it may be an s.c.s. during formation.

When we think about a black hole, we usually imagine by default the kind of eternal black hole described by the Schwarzschild spacetime. Some significant difficulties occur even in this simplest possible case. As noted above, the singularity may have a completely different character than the singularity occurring during the gravitational collapse of an astrophysical black hole, and this leads to suspicion that by considering the Schwarzschild case, we are omitting essential considerations.

Hawking and Ellis, have a nice discussion along these lines, including an example similar to the one above, in section 8.3, "The description of singularities," p. 276:

Hawking and Ellis have a nice discussion along these lines, including an example similar to the one above, in section 8.3, "The description of singularities," p. 276:

The chances for a more definitive answer might be better in the case of a naked singularity. Such a singularity can exist in both the past light cone and the future light cone of an observer, so one can imagine doing experiments on it and finding the results. In this sense it may be more likely to have measurable properties.