If one of two entangled particles passes the event horizon of a black hole, it effectively becomes inaccessible to observers outside the event horizon. This situation poses interesting questions and challenges related to quantum entanglement and the fate of entangled particles.
According to our current understanding of black holes and quantum mechanics, when a particle passes beyond the event horizon, it is thought to become irretrievable. The gravitational pull of the black hole is so strong that not even light can escape from within the event horizon. Consequently, any information or particles inside the event horizon cannot be directly observed or accessed by an observer outside the black hole.
When two particles are initially entangled, their entanglement remains intact even if one of them crosses the event horizon. The entanglement is a property of the quantum state of the particles and is not affected by their spatial separation. However, since the information about the entangled state cannot escape the event horizon, the entanglement becomes "trapped" inside the black hole.
From the perspective of an observer outside the black hole, the entanglement is effectively lost. This is because any attempts to measure or interact with the particle inside the black hole would require crossing the event horizon, which is not possible. Consequently, the observer outside the black hole would no longer have access to the entangled information associated with the particle inside the black hole.
The fate of entangled particles separated by an event horizon is an active area of research and an open question in the study of quantum gravity. The relationship between quantum mechanics and black hole physics is an area of ongoing investigation, and scientists are exploring the possible implications of entanglement in the context of black holes through theoretical studies and thought experiments.