What is the divergence and curl at the edge of a black hole?
Divergence and curl of what?
Whatever black holes continually suck into themselves continually
Did you tried to say something like " the linear momentum and angular momentum of a mass crossing the horizon of a BH"? For instance, divergence would be useful for studying if there are sources or sinks in a field (for a BH the divergence of the gravitational field is negative as usual).
the div and curl of most things at the edge of a black hole is nothing special, since this is the event horizon.
Div and curl operate on vector fields, not "whatevers". You need to specify what vector field for this even to be a question.
At the risk of sounding like a broken record, let me recommend Schey's Div, Grad, Curl and All That.
Am I missing something? I really don't know anying about GR but to capture the black holeness wouldn't you have to work in 4-space. The cross product is not defined in 4 dimensions.
wedge product is the generalization of the cross product to higher dimensions:
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