When an entangled particle falls into a black hole, the entanglement between that particle and its partner will be disrupted or lost from the perspective of an observer outside the black hole. This is due to the extreme gravitational forces and the presence of an event horizon, which is the boundary beyond which nothing can escape the gravitational pull of the black hole.
According to our current understanding of black holes and quantum mechanics, information cannot be transmitted from inside a black hole to an observer outside. This principle is known as the "no-hair theorem" and implies that the black hole's characteristics, such as its mass, charge, and angular momentum, are the only observable properties.
As the entangled particle crosses the event horizon, it becomes inaccessible to any outside observers. From their perspective, the entanglement is effectively lost. The fate of the particle inside the black hole is a subject of ongoing theoretical investigation, as it is still an open question how quantum mechanics and gravity interact under such extreme conditions.
It's worth noting that the behavior of quantum entanglement in the presence of a black hole is an active area of research in theoretical physics, particularly in the study of black hole information paradox and the field of quantum gravity. Different proposed resolutions, such as the holographic principle or black hole complementarity, aim to reconcile quantum mechanics and general relativity in the context of black holes.