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G'Day Mark !
Welcome back !!
I'm not a very good answerer of these kinds of questions (other folk are more qualified) but it seems to me that the force due to gravity around a black hole (or any other matter dense body) is directed inwards, towards the centre.
If the hole is rotating, then I would think that the net resultant direction, due to gravity would be along curved lines, as this kind of BH drags spacetime with it, (outside of the event horizon).
I don't see the need for extra dimensions in all of this.
Also, the Event Horizon is unnoticeable to a falling body. It is only noticed by an observer. I think a photon is theorised to move in curved world lines inside the Event Horizon … (but this can still be envisaged within the normal three dimensions).
Over to others.
Good to have you back.
Cheers
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