Topology of de Sitter and black hole

  1. What does it mean in the statement "Topologically, de Sitter space is R × S^n-1..."
    What is the topology of a Schwarzschild black hole?
  2. jcsd
  3. George Jones

    George Jones 6,476
    Staff Emeritus
    Science Advisor
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    Every spacetime is a differentiable manifold, and every differentiable manifold is a topological space. The underlying topoogical space for de Sitter spacetime is the topological product R x S^3. Here, R is the set of real numbers, and is, roughly, a space of time coordinates. S^3, the compact 3-dimensional hypersurface of a 4-dimensional ball, is a space of spatial coordinates.

    R^2 x S^S. Here, S^2 is the 2-dimesional surface of a 3-dimensional ball, and represents the spherical symmetry of Schwarzschild spacetime. R^2 is the set of ordered pairs of real numbers, and is the space of t and r coordinates.

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