Physical Relevance of Singularity Theorems?

[strangerep]

I've been reading this recent review paper by Senovilla & Garfinkle on The 1965 Penrose singularity theorem.

In sect 8.3 (p38):

[...] the existence of a positive cosmological constant $\Lambda>0$, which is just the wrong sign for the curvature condition (6) used in the focusing effect and, ultimately, in most singularity theorems.

Their eqn(6) is on p8: $R_{\rho\nu} u^\rho u^\nu ~\ge~ 0 ~.$

The message I take away from this is that much of the theory about singularity theorems has turned out to be irrelevant to the real world.

Or am I missing something?

 

[PeterDonis]

The message I take away from this is that much of the theory about singularity theorems has turned out to be irrelevant to the real world.

I would say might turn out to be irrelevant to the real world. It depends on how the various proposed "no singularity" solutions for the early universe and for black holes (actually "apparent" black holes if the proposals work out, since the proposed solutions contain no event horizons, only apparent horizons) pan out. If they work out, then yes, it would be true that the singularity theorems only apply to solutions that turn out not to describe the real world--in the solutions that describe the real world, key assumptions that go into the singularity theorems are violated (mainly the energy conditions).

 

[robphy]

One could argue that an additional contribution of the singularity theorems is that it they frame how to think about the general problem of singularities ( not tied to a particular class of solutions ). If more cases are needed, then they may arise as variations of existing theorems... possibly with different ways of imposing conditions needed to complete the proofs.

 

[strangerep]

Hmm. Wishful thinking?

(Anyway, thanks for the comments. )

 

[robphy]

Possibly related discussion:
http://physics.stackexchange.com/qu...gularities-if-there's-a-positive-cosmological

https://www.google.com/search?q=singularity+theorem+positive+cosmological+constant