I Are there non-smooth metrics for spacetime (without singularities)?

AI Thread Summary
The discussion centers on the possibility of non-smooth metrics for spacetime that do not involve singularities. It highlights that local Lorentz symmetry, crucial in general relativity (GR), would be violated if spacetime is not smooth, undermining the principle of equivalence. The participants express skepticism about the existence of non-smooth spacetimes compatible with current physical theories, as such configurations typically lead to singularities and geodesic incompleteness. The consensus suggests that any deviation from smoothness would conflict with established principles in GR, making non-smooth metrics implausible. Ultimately, the dialogue emphasizes the foundational role of smoothness in maintaining the integrity of spacetime in physics.
Suekdccia
Messages
352
Reaction score
30
TL;DR Summary
Are there non-smooth metrics for spacetime (that don't involve singularities)?
Are there non-smooth metrics for spacetime (that don't involve singularities)?

I found this statement in a discussion about the application of local Lorentz symmetry in spacetime metrics:

Lorentz invariance holds locally in GR, but you're right that it no longer applies globally when gravity gets involved. While in SR, quantities maintain Lorentz (or Poincare) symmetry via Lorentz (or Poincare) transforms, in GR they obey general covariance which is symmetry under arbitrary differentiable and invertible transformations (aka diffeomorphism).
If a spacetime was not smooth, and didn't allow local Lorentz symmetry, it would break the principle of equivalence which is the bedrock assumption in GR.


I would like to know if there are possible spacetimes where they would not be smooth. The only problem is that this usually involves singularities. Are there models or metrics of non smooth spacetimes that would be compatible with what we currently know in physics but that don't necessarily involve singularities?
 
Space news on Phys.org
Suekdccia said:
I found this statement in a discussion
Where? Please give a reference.
 
  • Like
Likes Vanadium 50
I'm trying to figure out what a non-smooth spacetime is supposed to be if it is not singular at the discontinuities.
 
Last edited:
In GR, the primary definition of singularity is geodesic incompleteness. A point of spacetime where all derivatives are undefined while continuity exists must lead to geodesic incompleteness, since geodesics require satisfaction of a differential equation. So such points necessarily lead to spacetime singularities as defined in GR.

As to the question: "Are there models or metrics of non smooth spacetimes that would be compatible with what we currently know in physics", irrespective of singularities, the answer must be no. As your quote notes, local Lorentz invariance would be violated, and all currently accepted theories require this, and all data are consistent with this.
 
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
The formal paper is here. The Rutgers University news has published a story about an image being closely examined at their New Brunswick campus. Here is an excerpt: Computer modeling of the gravitational lens by Keeton and Eid showed that the four visible foreground galaxies causing the gravitational bending couldn’t explain the details of the five-image pattern. Only with the addition of a large, invisible mass, in this case, a dark matter halo, could the model match the observations...
Hi, I’m pretty new to cosmology and I’m trying to get my head around the Big Bang and the potential infinite extent of the universe as a whole. There’s lots of misleading info out there but this forum and a few others have helped me and I just wanted to check I have the right idea. The Big Bang was the creation of space and time. At this instant t=0 space was infinite in size but the scale factor was zero. I’m picturing it (hopefully correctly) like an excel spreadsheet with infinite...
Back
Top