What a black hole does to a light cone

Throw an apple. It rises five metres and comes back in two seconds, and its path through spacetime, drawn with the time axis to scale so that two seconds is 605,000 kilometres, is an arc of radius c²/g: just under one light-year, straight to eight parts in a billion. The apple does not feel the bend. Neither will you.

One quantity, all the way down

In flat space light runs at 45° and the cone splits everything into what you can reach and what you can only watch. Mass leans it. The outgoing edge tips off 45° by exactly arctan(r_s/r), and nothing else ever happens.

Nothing is at the horizon

At 45° the outgoing edge stands straight up. No wall, no jolt, no marker. At M87* the tide trying to pull you apart as you cross is 5 × 10⁻¹¹ g, so what changed is only which futures are still on the list.

Every direction you can still point

Past it the edge leans the other way, and every direction the cone allows has r falling. Leaving is not difficult here, it is earlier: the same impossibility as going back to yesterday. Turn the ship around and fire. The engines light, the ship turns, and r keeps falling. The stars you left keep arriving the whole way down, and none of them is anywhere you can go.

The clock

The longest anyone gets between the horizon and the centre is πGM/c³: 328 microseconds at Cygnus X-1, 66 seconds at Sgr A*, 28 hours at M87*. Arriving from far away instead of crossing at rest leaves you 4GM/3c³, which is 4/(3π) of it, so most of your time is gone before you arrive. Firing the engines takes more still. Halving what is left costs 3,000 g at M87* and 10¹² g at Cygnus X-1, and neither buys a metre.

A moment, not a place

The visualisation keeps distances honest and leans the cones. A Penrose diagram makes the opposite trade: every cone goes back to 45°, and everything else is distorted to pay for it. Drawn that way, the centre comes out horizontal, a moment lying across the whole width of the inside.