tl:dw: Gravity propagates at the speed of light, but the mass causing the gravity is trapped under an event horizon that not even light can escape, so how do gravity escape the event horizon.
There's a few explanations that all end up at the same result:
- Gravity warps the fabric of spacetime, but each bit of spacetime is only influenced by it's neighboring bits. So spacetime is still able to get dragged towards the singularity in the same way that a water molecule gets dragged towards a waterfall.
- If gravity is a quantum field, then the force of gravity would be mediated by virtual particles of the gravitational force carrying particle (known as the graviton). Virtual particles (on account of them being more mathematical artifacts than real things that exist) can travel at any speed, including at infinite speed, so the virtual gravitons wouldn't be stopped by the event horizon.
- From the frame of reference of an outside observer, anything approaching a black hole takes an infinite amount of time to cross the event horizon, therefore all mass that has ever fallen into a black hole (including the mass of the star that turned into the black hole) is still outside the event horizon for anyone also outside the event horizon. This means that the gravitational influence of all that mass is still causally connected with any outside observers, and thus they would still feel the gravity of said mass.
As Pratchett remarked, when a king dies his heir immediately becomes king. Like, instantaneously as soon as the king is dead. "The king is dead, long live the king". It's faster than light.
So one way you could do it is packing your probe you launch inside the black hole with thousands and thousands of live kings, each one bit of information. Then the probe selectively guillotine them mechanically, and you watch the thousands and thousands of heirs outside of the black hole, checking if they're now kings, to decode your message.
It's foolproof. And if it doesn't work then you've still got a ton of the monarchy either dead or marooned in space so really it's a win-win.