Röntgen-Grobstrukturuntersuchungen an Polyurethan-Schaumstoffen

Holographic entanglement plateaux

“…Note that in this collapsed black hole context, the homology requirement is satisfied automatically, though as explained in [12], that itself leads to very curious feature of entanglement entropy: it can distinguish between an eternal black hole and a collapsed one, arbitrarily long after the collapse had taken place [41]. In this sense, while in the AdS/CFT context we are used to classical bulk surfaces providing at best only some coarse-grained CFT information, the homology requirement induces a fine-grained aspect to the entanglement entropy observable.…”

“…In particular, in the HRT prescription of computing entanglement entropy via a smallest area extremal surface, the continuity argument given in §2 does not apply. It would be interesting to explore whether sufficient time-dependence can provide counter-examples to continuity or whether the one can generalize the proof of continuity to the Lorentzian context; we leave further investigation of this issue for the future [12].…”

“…In fact, as we indicate in §7, in time dependent examples the situation may be much more intricate and will be discussed elsewhere [12]. 2 Earlier studies of holographic entanglement entropy have indeed revealed examples where S(α) undergoes a first order phase transition, i.e., ∂ α S(α) is discontinuous due to change in the nature of the minimal surfaces [15,16].…”

“…The result for the entanglement entropy of a free neutral Dirac fermion c = 1 was derived in [19] and was extended to a grand canonical density matrix including a U (1) chemical potential in [25]. 12 In either case we can use the resulting expressions (which being rather long we refrain from reproducing here) to understand the behaviour of the entanglement in the system. Using the explicit expressions one can check that the resulting answer exhibits no sharp feature.…”

“…the turning point, furthest away from the boundary) of any extremal surface which is fully anchored on (a single) AdS boundary cannot occur inside a black hole. On the other hand, in time-dependent spacetimes, there do exist extremal surfaces anchored on the boundary which penetrate past the horizon[12,[29][30][31][32][33]. For this reason, entanglement entropy is cognizant of some physics inside the horizon.…”