- #31
- 22,823
- 14,864
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
- Start date
Click For Summary
Discussion Overview
The discussion centers on whether Minkowski spacetime can be considered a solution to the Friedmann Equations, particularly in the context of different curvature parameters and their implications for the nature of the universe. Participants explore the relationships between static and expanding models, coordinate transformations, and the interpretation of curvature in cosmological models.
Discussion Character
- Debate/contested
- Technical explanation
- Conceptual clarification
Main Points Raised
- Some participants note that the empty FRW universe with curvature parameter ##k = -1## is mathematically equivalent to the Milne universe, which also expands linearly.
- Others argue that Minkowski space is not a different solution but rather the same solution expressed in different coordinates, similar to the difference between Cartesian and polar coordinates in Euclidean space.
- A participant questions the relationship between the static Minkowski spacetime and the Friedmann solutions, expressing confusion about the implications of ##H = 0## and ##k = 0## in the context of an empty universe.
- Some participants clarify that the parameter ##k## is coordinate-dependent and does not represent a physical property of the universe, leading to discussions about the intrinsic and extrinsic curvature of spacelike surfaces.
- There is a technical exploration of how different coordinate choices can yield different interpretations of the same spacetime geometry, particularly in the context of the Milne universe and Minkowski spacetime.
- One participant shares a mathematical derivation to illustrate the equivalence of the expanding universe and Minkowski space under certain coordinate transformations.
- Another participant expresses difficulty in understanding some of the technical details discussed, particularly regarding coordinate dependence in cosmological interpretations.
Areas of Agreement / Disagreement
Participants express differing views on whether Minkowski spacetime can be considered a solution to the Friedmann Equations, with some asserting that it is equivalent to other solutions under different coordinates, while others remain uncertain about the implications of curvature parameters and their physical interpretations. The discussion does not reach a consensus.
Contextual Notes
The discussion highlights the complexity of interpreting curvature parameters and the role of coordinate systems in cosmological models. There are unresolved questions regarding the physical significance of ##k## and the nature of solutions to the Friedmann Equations.
Similar threads
- · Replies 6 ·
- · Replies 17 ·
- · Replies 6 ·
- · Replies 1 ·
- · Replies 27 ·
Undergrad
Friedmann Equation - Positive Curvature
- · Replies 12 ·
- · Replies 3 ·
- · Replies 9 ·
- · Replies 27 ·
- · Replies 1 ·