A Physical Relevance of Singularity Theorems?

strangerep
Science Advisor
Messages
3,766
Reaction score
2,213
I've been reading this recent review paper by Senovilla & Garfinkle on The 1965 Penrose singularity theorem.

In sect 8.3 (p38):
Senovilla & Garfinkle said:
[...] 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? :oldconfused:
 
Physics news on Phys.org
strangerep said:
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).
 
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.
 
Hmm. Wishful thinking? :rolleyes:

(Anyway, thanks for the comments. :oldbiggrin: )
 
Thread 'Can this experiment break Lorentz symmetry?'

Thread 'Can this experiment break Lorentz symmetry?'

1. The Big Idea: According to Einstein’s relativity, all motion is relative. You can’t tell if you’re moving at a constant velocity without looking outside. But what if there is a universal “rest frame” (like the old idea of the “ether”)? This experiment tries to find out by looking for tiny, directional differences in how objects move inside a sealed box. 2. How It Works: The Two-Stage Process Imagine a perfectly isolated spacecraft (our lab) moving through space at some unknown speed V...
View full post »

Thread '1-Way Speed of Light'

Does the speed of light change in a gravitational field depending on whether the direction of travel is parallel to the field, or perpendicular to the field? And is it the same in both directions at each orientation? This question could be answered experimentally to some degree of accuracy. Experiment design: Place two identical clocks A and B on the circumference of a wheel at opposite ends of the diameter of length L. The wheel is positioned upright, i.e., perpendicular to the ground...
View full post »

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »

Similar threads

Were Hawking Radiation & Singularity Theorem Controversial in 1965?
Replies
2
Views
2K
BRS: The FRW Dust with E^3 Hyperslices
Replies
11
Views
2K
Dark Energy, the Cosmological Constant, General Relativity and you
Replies
13
Views
5K
Remark on electric charge Lorentz invariance
Replies
1
Views
3K
Mathematica This Week's Finds in Mathematical Physics (Week 264)
Replies
6
Views
4K
Mathematica This Week's Finds in Mathematical Physics (Week 226)
Replies
7
Views
3K
Mathematica This Week's Finds in Mathematical Physics (Week 226)
Replies
7
Views
4K

Hot Threads

Recent Insights

Back
Top