What is the metric for a bag-of-gold spacetime?

In summary, the metric for a bag-of-gold spacetime is a mathematical representation of the geometry of spacetime in a hypothetical universe where space and time are discrete and finite. It describes the relationships between the coordinates and the curvature of spacetime, and is used in theoretical physics to study the behavior of particles and objects in this type of universe. This metric is based on the concept of a lattice, with points representing the discrete units of space and time, and can be used to calculate distances, angles, and other physical properties in this unique spacetime.
  • #1
Onyx
120
3
TL;DR Summary
What is the metric for a bag-of-gold spacetime?
What is the metric for a bag-of-gold spacetime?
 
Physics news on Phys.org
  • #2
Onyx said:
What is the metric for a bag-of-gold spacetime?
There is no simple expression for the metric for this spacetime, since it consists of (at least) two regions with very different properties that are "glued" together. However, a good mathematical treatment can be found in section III (b) of this paper:

https://arxiv.org/abs/0803.4212

Note, though, that this paper requires "A" level background knowledge to properly understand. A "B" level discussion of the "bag of gold" spacetime and its implications is not really possible.
 
  • Like
Likes Demystifier
  • #3
PeterDonis said:
There is no simple expression for the metric for this spacetime, since it consists of (at least) two regions with very different properties that are "glued" together. However, a good mathematical treatment can be found in section III (b) of this paper:

https://arxiv.org/abs/0803.4212

Note, though, that this paper requires "A" level background knowledge to properly understand. A "B" level discussion of the "bag of gold" spacetime and its implications is not really possible.
Is that because the gluing process is so complicated?
 
  • #4
Onyx said:
Is that because the gluing process is so complicated?
Not really, the black hole interior can be interpreted as a "bag of gold" even without gluing. See https://arxiv.org/abs/1411.2854
 
  • Like
Likes ohwilleke and Ibix
  • #5
Demystifier said:
Not really, the black hole interior can be interpreted as a "bag of gold" even without gluing. See https://arxiv.org/abs/1411.2854
Am I correct in assuming that it is just like the OS collapse case, where there has to be two different metrics for two different manifolds? Also, if not a bag of gold, what is this person describing (not a reliable source)?
 
  • #6
Onyx said:
Am I correct in assuming that it is just like the OS collapse case, where there has to be two different metrics for two different manifolds?
What's OS?
 
  • #9
Onyx said:
Is that because the gluing process is so complicated?
Not really, no. The diagrams in Fig. 3 of the paper are fairly straightforward to understand. But the mathematical details required to verify that everything actually can fit together the way those diagrams depict while satisfying the Einstein Field Equation are not.
 
  • #10
Onyx said:
Am I correct in assuming that it is just like the OS collapse case, where there has to be two different metrics for two different manifolds?
The "gluing" process at the boundary between two regions follows the same general rules in both cases, yes. But the relationship between the regions is not the same in the two cases.

In the OS case, we have a Schwarzschild region extending in from infinity, with ##r## (the areal radius) decreasing monotonically, to a boundary with a closed FRW region, and the closed FRW region occupies the rest of the spacetime, with ##r## continuing to decrease to ##r = 0##.

In the "bag of gold" case described in Fig. 3 of the paper, we have a Schwarzschild region extending in from infinity all the way through an Einstein-Rosen bridge, where ##r## (the areal radius) reaches a minimum, and then ##r## increasing again to a boundary with a closed FRW region, in which ##r## continues to increase to some maximum value (given as ##a_{12}## in the diagram) and then decreases again. (The spacetime could end with that first FRW region decreasing to ##r = 0##, but in Fig. 3 of the paper, it doesn't, there is a second Schwarzschild region going through a second Einstein-Rosen bridge and connecting to a second FRW region that ends by decreasing to ##r = 0##. In principle you could have any number of such transitions added on.)
 

Similar threads

  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
Replies
11
Views
2K
  • Special and General Relativity
2
Replies
40
Views
944
  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
Replies
11
Views
382
  • Special and General Relativity
Replies
21
Views
2K
  • Special and General Relativity
Replies
3
Views
1K
  • Special and General Relativity
Replies
13
Views
1K
  • Special and General Relativity
Replies
4
Views
939
Back
Top