s^2 = r^2 - t^2,
That's treating a time dimension as a vastly different type dimension to a space one. Arguably the case, but when considering the dimensions as all 'spacetime' dimensions (e.g. as 'seen from the outside' as one glorious tapestry), then you can't treat it as a different type of dimension
in the equation and so you treat it differently by giving it an imaginary relationship to the rest. (a^2 - b^2) = (a^2 + (i.b)^2), so it's the same algabraicly, but (as it was explained to me) important when it comes to wokring it out conceptually.
What you then go on to say about computability within an EH is perhaps true. (Or certainly, given that some of our best minds are working out what's happening.) But the space-time slope becoming greater than 'c' (by the appropriate measure) creates a zone where "the laws of physics as we know them need not apply" more than the slope->lim(infinity) parts do.
I hesitate to describe it in the same terms as breaking the sound barrier, given the lack of actual medium involved and thus not laminar flows and fluid dynamics and shockwaves
per se, but suitable considerations as to what effects
might exist should be taken.
So, we can currently handle both subsonic and supersonic flight dynamics with an overall set of equations, even if we may generalise them to "these are simpler ones that apply to subsonic, and these are the ones that apply to supersonic" and then when working with ramjets and scramjets we either go back to the complex ones that encompass both behaviours or fudge the interface. Right now, we (humanity) are probably closer to the immediately pre-supersonic airodynamicists who can speculate about the interface between the two modes of flight, and guess what would happen 'on the other side', but it's guesswork until some equivalent of Theodore Karman arises. Hawking or one of his contemporaries might already be due that title, but I don't think we'll know for sure until we have the ability to produce a Chuck Yeager equivalent. Who can also report back!