The behavior of entangled particles in extreme scenarios such as one particle entering a black hole, being annihilated with an antiparticle, or engulfed in vacuum decay is a subject of ongoing scientific research and speculation. there is no definitive consensus on what precisely happens to entanglement under such extreme conditions. However, I can provide you with some insights based on our current understanding.
Entanglement and Black Holes: When one entangled particle enters a black hole, the fate of its entanglement with the other particle outside the black hole is not well understood. According to general relativity, information that falls into a black hole is thought to be lost forever, leading to the "information paradox." This poses challenges to the preservation of entanglement across the black hole event horizon. Some theories propose that the entanglement may be "scrambled" or redistributed in a complex way, making it difficult to recover the original entangled state.
Entanglement and Particle Annihilation: If one particle of an entangled pair is annihilated with its corresponding antiparticle, it would likely disrupt the entanglement between them. Annihilation typically results in the conversion of mass into energy, and any entanglement between the particles would likely be destroyed in the process.
Entanglement and Vacuum Decay: Vacuum decay is a speculative concept in theoretical physics that involves a sudden and catastrophic change in the structure of empty space (vacuum) at a fundamental level. If one entangled particle were to be engulfed in vacuum decay, it would likely disrupt the entanglement with its partner outside the decayed region. The exact implications of vacuum decay on entanglement are not well understood and would depend on the specific nature of the decay process.
It's important to note that the scenarios you mentioned involve extreme and poorly understood physical phenomena. The behavior of entanglement in such scenarios may require a deeper understanding of quantum gravity and the interplay between quantum mechanics and general relativity. Current research and future theoretical advancements will likely provide further insights into these intriguing questions.