GR: Is Schwarzschild Spacetime Time-Independent?

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Discussion Overview

The discussion centers around the significance of time-independence in Schwarzschild spacetime within the context of General Relativity (GR). Participants explore the implications of the metric's time-independence versus the time-dependence of the embedding that describes the manifold's shape.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants express confusion regarding the significance of the time-independent metric of Schwarzschild spacetime compared to the time-dependent embedding of the manifold.
  • One participant suggests that the metric is more significant because it allows for a family of timelike worldlines that do not change over time for a specific set of observers.
  • Another participant questions which embedding is being referred to and requests links to previous discussions for clarity.
  • Links to previous posts and external resources are provided, discussing embeddings of Schwarzschild spacetime in higher-dimensional spaces, with a claim that this topic is unrelated to GR.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the significance of the metric versus the embedding, indicating a debate over the interpretation and relevance of these concepts in the context of GR.

Contextual Notes

There are references to previous discussions and external literature, but the relevance of these embeddings to the core concepts of GR remains unresolved.

jk22
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I'm a bit confused about GR : what is more significant about the considered spacetime, the metric, which is time-independent, or the embedding (there are already some posts on PF about it), which describes the shape of a manifold, but is time-dependent ?
 
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jk22 said:
what is more significant

That depends on what you consider "significant".

jk22 said:
the metric, which is time-independent

More precisely, the spacetime geometry admits a family of timelike worldlines (which can represent a family of observers) along which the spacetime geometry does not change (and therefore the spacetime geometry "looks the same" at all times to that family of observers).

jk22 said:
the embedding (there are already some posts on PF about it), which describes the shape of a manifold, but is time-dependent ?

What embedding are you referring to? Links to the PF posts you mention would help.
 
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