How can there be an out flow from a black hole??
Hawking radiation - British physicist Stephen Hawking used quantum field theory in curved space-time to build this argument.
This theory shows that vacuum in quantum field theory is not really empty; it’s filled with “virtual pairs” of particles and antiparticles that pop in and out of existence, with lifetimes determined by the Heisenberg uncertainty principle. When such pairs forms near the event horizon of a black hole, though, they are pulled apart by the tidal forces of gravity. Sometimes one member of a pair crosses the horizon and can no longer recombine with its partner. The partner can then escape to infinity, and since it carries off positive energy, the energy (and thus the mass) of the black hole must decrease. This escaping partner is the radiation.
A down-to-earth example of the existence of these particles is used to explain the Casmir Effect.
https://en.wikipedia.org/wiki/Casimir_effect
A black hole exhibits three properties: mass, charge, and spin. So it produces gravity and a magnetic field. The spin produces frame dragging, which is more complicated.
Once matter crosses the Event Horizon, you are correct.
However, matter that is near the Event Horizon is squished and elongated (spaghettified) and in friction with literally billions of tons of other matter heating it up to extremely high temps as it circles the drain, it gives of radiation in the form of radio waves, X-Rays, and microwaves and magnetic fields that are twisted and knotted in unimaginable forms..................