Erin Brierly - Solemn shade CC
Nirvana - where time stands still
For a distant observer, measured time slows to a standstill as an object approaches the event horizon of a Schwarzschild black hole.
With the new solution proposed here, every point inside the event horizon of a black hole is sitting on a local event horizon, where, for a distant observer, measured time would slow to a standstill (if it were visible). This follows because the metric function in Schwarzschild coordinates will always approach infinity at each (local) event horizon. When considering the path of an object falling 'through' the event horizon, one has to consider what happens to that path once time stands still. Further movement becomes impossible, so all paths terminate at the event horizon. In no sense does this violate Einstein's equivalence principle. Just treat infinity as a limit: with the metric approaching infinity, time slows down at an ever decreasing rate. A particle approaching the event horizon would still be obeying the equivalence principal all the way until further movement ceases entirely. In the limit, this must still be true. As time ceases to make further progress, there will be no further movement whatsoever, but an observer falling towards an event horizon would be completely unaware of this as their body clock slows to a standstill. A different concern sometimes raised is the idea of infinity, as it were, just hanging in space. In fact, this idea is also a mistake. These points are at infinity on the time axis and should cause no more undue concern than similar points at infinity on the extremities of other axes.
Now let us now look at the special properties of a body without the progress of time.