3 research outputs found
Entanglement entropy in de Sitter: no pure states for conformal matter
In this paper, we consider the entanglement entropy of conformal matter for
finite and semi-infinite entangling regions, as well as the formation of
entanglement islands in four-dimensional de Sitter spacetime partially reduced
to two dimensions. We analyze complementarity and pure state condition of the
entanglement entropy of pure states and show that they never hold in the given
setup. We consider two different types of Cauchy surfaces in the extended
static patch and flat coordinates, correspondingly. For former, we found that
entanglement entropy of a pure state is always bounded from below by a constant
and never becomes zero, as required by quantum mechanics. In turn, the
difference between the entropies for some region and its complement, which
should be zero for a pure state, in direct calculations essentially depends on
how the boundaries of these regions evolve with time. Regarding the flat
coordinates, it is impossible to regularize spacelike infinity in a way that
would be compatible with complementarity and pure state condition, as opposed,
for instance, to two-sided Schwarzschild black hole. Finally, we discuss the
information paradox in de Sitter and show that the island formula does not
resolve it. Namely, we give examples of a region with a time-limited growth of
entanglement entropy, for which there is no island solution, and the region,
for which entanglement entropy does not grow, but the island solution exists.Comment: v1: 25 pages, 10 figures; v2: 25 pages, 10 figures, references added,
notation clarifie
Entanglement Islands and Infrared Anomalies in Schwarzschild Black Hole
In this paper, island formation for entangling regions of finite size in the
asymptotically flat eternal Schwarzschild black hole is considered. We check
the complementarity property of entanglement entropy which was implicitly
assumed in previous studies for semi-infinite regions. This check reveals the
emergence of infrared anomalies after regularization of a Cauchy surface. A
naive infrared regularization based on ``mirror symmetry'' is considered and
its failure is shown. We introduce an improved regularization that gives a
correct limit agreed with the semi-infinite results from previous studies. As
the time evolution goes, the endpoints of a finite region compatible with the
improved regularization become separated by a timelike interval. We call this
phenomenon the ``Cauchy surface breaking''. Shortly before the Cauchy surface
breaking, finite size configurations generate asymmetric entanglement islands
in contrast to the semi-infinite case. Depending on the size of the finite
regions, qualitatively new behaviour arises, such as discontinuous evolution of
the entanglement entropy and the absence of island formation. Finally, we show
that the island prescription does not help us to solve the information paradox
for certain finite size regions.Comment: v1: 55 pages, 19 figures; v2: 57 pages, 19 figures, references added,
Sec. 5 presentation improve