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I am just getting round to taking another look at the Kruskal extension. The last time I looked, I had many problems with it, at least the way it was presented, as it had quantities under square root signs that became negative. And that wasn't the only problem. It basically transforms only the r and t terms, and leaves the terms in theta and phi as is to get "Mixed Edington-Finkelstein coordinates". However that does not allow construction of a 4d metric that I can recognize as supporting our physics. To be able to unequivocally say that a metric represents a universe like ours, it should be possible to get it in the formJesseM said:No, this is just an artifact of the way Schwarzschild coordinates work, you're free to use a coordinate system where there is no "switch" and the time coordinate continues to be physically timelike inside the event horizon, such as Kruskal-Szekeres coordinates.

a^2(t)(dx^2 + dy^2 + dz^2) - (cdt)^2

i.e. Minkowski with some tolerable rate of expansion or contraction

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