midtskogen wrote:Source of the post If you cross the event horizon at an angle, would that change?
Yes. It would become shorter.
Here I've rendered an animation to show this surprising result. We drop in from 5 times the horizon radius of the black hole SgrA*, at first starting perfectly from rest, but then with more and more sideways velocity until we reach an orbit. The top image is our path, with dashed surfaces representing the black hole's innermost stable circular orbit (ISCO) in red, the photon orbit in yellow, and the horizon in black. At lower left is our distance from the singularity vs time (as measured by our own clock as we make this journey). A vertical line marks passing through the horizon, and the time from the horizon to singularity is displayed in the corner. Finally, at bottom right is the "effective potential", which is the imagined landscape describing how gravity accelerates us when taking into account our angular momentum and general relativistic effects.
Plunging straight in with no angular momentum, the time we experience from horizon to singularity is 30 seconds. As we add more sideways speed, this time experienced below the horizon shrinks down to just 15 seconds. Finally when we have enough angular momentum to make an orbit, we discover it isn't an ellipse, but a more unusual shape.
The shape of the potential also changes as we add more angular momentum. At first it's a simple funnel dropping down, but angular momentum causes the outer part to flatten out (slowing our plunge inward), with a hill eventually rising up which causes us to turn around and reach orbit. Meanhwhile, however, the inner part of the potential is growing steeper, so for as long as we fall through the horizon, that extra sideways speed makes us paradoxically reach the singularity sooner.
And thus my favorite way of describing black holes is that they are like quicksand. Once caught by it, then the more you struggle, the faster you sink!