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1. B Is there anything left after a black hole is done evaporating?

Suppose a black hole isn't sucking in any new material. Then it is doomed to evaporate due to Hawking radiation and become smaller and smaller over time. Is there anything left when it's done evaporating?
2. A Black Hole Topology

It seems that in order to make my question less muddy I would need to study GR a bit myself first.
3. A Black Hole Topology

Well, add the point at infinity to the real line and you are in business. I have no idea if that makes any physical sense though. The space S^2xS^1 is the complement of the unknot with no framing. The associated invariants are easy to compute. Unfortunately nothing interesting falls out as I...
4. A Black Hole Topology

I want to understand the topology of a black hole so that I can think about how (or if it's even possible) to compute its Witten-Reshetikhin-Turaev invariant.
5. A Black Hole Topology

I'm not sure about the physics term so maybe I should have stuck with the math. By cross section, I mean one of the boundaries of a cobordism between two 3-manifolds.
6. A Black Hole Topology

Can a black hole be presented as a Heegaard decomposition or as the complement of a knot? I'll try and elaborate: If I understand correctly, the cross section of spacetime near a black hole can be thought of topologically as a manifold. What manifold is it? Can the manifold be decomposed?
7. I Simple GR Question

OK, I think I get it now. Thanks everyone!
8. I Simple GR Question

I'm referring to ##g## in two different contexts which is what I think made my question unclear. So, let ##g## be the metric from GR and let ##d## be the metric from math class. Does defining ##g## on a differentiable manifold automatically induce ##d##? As an aside, this is interesting to me...
9. I Simple GR Question

You're right, I suppose I should make that precise. The metric topology I'm referring to has as open sets ##B_r(m_0)=\{m_0\in M : g(m_0,m)<r\ \forall m\in M \text{ where } r>0\}##
10. I Simple GR Question

Is it fair to say, when talking about spacetime with a given metric, it would be redundant to state that the associated set has the metric topology placed on it. In other words, let ##M## be a set, ##O## the metric topology, ##\nabla## a connection, ##g## a metric, and ##T## be the direction of...