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I think it should be stressed that that manifold is a hyperbolic space, not a hyperboloid. These are not the same thing.PAllen said:
Is Minkowski spacetime a solution of the Friedmann Equations?
- Context: Undergrad
- Thread starter timmdeeg
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SUMMARY
The discussion confirms that Minkowski spacetime is not a distinct solution of the Friedmann Equations but rather a coordinate transformation of the same solution. Specifically, the empty Friedmann-Robertson-Walker (FRW) universe with curvature parameter k = -1 is equivalent to the Milne universe, which also expands linearly. The parameters H = 0 and k = 0 do not yield a valid solution in the context of an empty universe, as densities are zero, leading to undefined curvature. The key takeaway is that both Minkowski and Milne spacetimes represent the same geometry, merely expressed in different coordinate systems.
PREREQUISITES- Understanding of Friedmann Equations in cosmology
- Familiarity with Minkowski spacetime and its properties
- Knowledge of coordinate transformations in general relativity
- Basic concepts of curvature parameters in cosmological models
- Study the implications of curvature parameters in cosmological models, focusing on k = 0 and k = -1
- Explore the mathematical foundations of coordinate transformations in general relativity
- Investigate the Milne universe and its relationship to Minkowski spacetime
- Learn about the implications of the Friedmann-Robertson-Walker metric in cosmology
Cosmologists, theoretical physicists, and students of general relativity seeking to deepen their understanding of the relationship between different cosmological models and their geometric interpretations.
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