Black hole entropy as entropy of entanglement, or it's curtains for the equivalence principle

Computer Science, University of York, York YO10 5DD, UK(Dated: July 7, 2009)The equivalence principle provides an important tenet of black hole physics: that a sufficientlysmall observer freely falling into a black hole should experience nothing special as she passes theevent horizon — the boundary of no return. Similarly, quantum fields impinging on a black holeshould exhibit no special behavior at the event horizon. Indeed quantum fields should be entangledacross the event horizon just as they would be across the boundary to any volume in flat space.We study this claim using random subsystems as models of black hole evaporation. We find thatunless the Bekenstein-Hawking entropy of a black hole is almost entirely entropy of entanglement,then the trans-event horizon entanglement vanishes long before the black hole has evaporated to thePlanck scale. This would force quantum fields across the event horizon to be arbitrarily far fromthe vacuum state; an energetic curtain would have descended around the black hole.