Discussion Overview
The discussion revolves around the topology of black holes, specifically exploring whether a black hole can be represented through Heegaard decompositions or as the complement of a knot. Participants examine the topological characteristics of the manifold associated with black holes, including various proposed models and their implications.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants propose that the cross section of spacetime near a black hole can be thought of as a manifold, but there is uncertainty about what is meant by "cross section."
- One participant states that the topological manifold describing the maximally extended Schwarzschild spacetime is ##S^2 \times R^2##, while a more physically reasonable model is ##R^4##.
- Another participant clarifies that a cobordism can only exist between compact manifolds, suggesting that the manifolds discussed are not compact.
- There is a suggestion to explore the topology of black holes to compute the Witten-Reshetikhin-Turaev invariant, although the feasibility of this is questioned.
- One participant introduces the idea of adding a point at infinity to the real line, but doubts its physical relevance.
- There is a discussion about the clarity of what is meant by "black hole topology," with questions about whether it refers to the entire spacetime, the event horizon, or other regions.
- Participants note that the connectedness of the black hole region depends on the specific spacetime being considered.
Areas of Agreement / Disagreement
Participants express differing views on the definitions and implications of black hole topology, with no consensus reached on the specific models or interpretations. The discussion remains unresolved regarding the clarity of terms and the physical relevance of proposed topological representations.
Contextual Notes
Limitations include ambiguity in the definitions of "cross section" and "black hole topology," as well as the dependence on the specific spacetime models being referenced. There is also uncertainty regarding the compactness of the manifolds discussed.
Who May Find This Useful
This discussion may be of interest to those studying general relativity, topology, and mathematical physics, particularly in relation to black hole theory and its mathematical implications.