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Onyx
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- What is the metric for a bag-of-gold spacetime?
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:Onyx said:What is the metric for a bag-of-gold spacetime?
Is that because the gluing process is so complicated?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.
Not really, the black hole interior can be interpreted as a "bag of gold" even without gluing. See https://arxiv.org/abs/1411.2854Onyx said:Is that because the gluing process is so complicated?
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)?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
What's OS?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?
This interpretation is rather contrived, though. I expressed my reservations about it in this previous thread: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
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.Onyx said:Is that because the gluing process is so complicated?
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.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?
A bag-of-gold spacetime is a theoretical concept in physics that describes a region of space where the gravitational field is so strong that it would be able to trap and hold a large amount of gold. It is a hypothetical scenario that is used in thought experiments and mathematical models to understand the behavior of gravity in extreme conditions.
The metric for a bag-of-gold spacetime is calculated using Einstein's field equations, which relate the curvature of space-time to the distribution of matter and energy. In this case, the distribution of matter is represented by the large amount of gold that is trapped within the gravitational field. The resulting metric describes the shape of space-time in this scenario.
Currently, there is no evidence to suggest that a bag-of-gold spacetime can exist in our universe. It is a purely theoretical concept that is used to explore the limits of our understanding of gravity. However, in the future, advancements in technology and our understanding of physics may allow us to observe or create such extreme gravitational fields.
The metric for a bag-of-gold spacetime differs from other metrics in that it describes a highly curved and dense region of space-time. This is due to the large amount of matter (gold) within the gravitational field. Other metrics may describe less extreme scenarios, such as the space-time around a planet or star.
Studying bag-of-gold spacetime can help us better understand the behavior of gravity in extreme conditions, which can have implications for our understanding of the universe and the laws of physics. It can also aid in the development of new theories and models that can be applied in other areas of physics, such as black holes and the early universe.