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Register a new userEntanglement degradation in multi-event horizon spacetimes
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Added by
Sourav Bhattacharya
Publication date
2021
fields
Physics
and research's language is
English
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We investigate the degradation of quantum entanglement in the Schwarzschild-de Sitter black hole spacetime, by studying the mutual information and the logarithmic negativity for maximally entangled, bipartite initial states for massless minimal scalar fields. This spacetime is endowed with a black hole as well as a cosmological event horizon, giving rise to particle creation at two different temperatures. We consider two independent descriptions of thermodynamics and particle creation in this background. The first involves thermal equilibrium of an observer with the individual Hawking temperature of either of the horizons. We show that as of the asymptotically flat/anti-de Sitter black holes, the entanglement or correlation degrades here with increasing Hawking temperature. The second treats both the horizons combinedly to define a total entropy and an effective equilibrium temperature. We present a field theoretic derivation of this effective temperature and argue that unlike the usual cases, the particle creation here is not ocurring in causally disconnected spacetime wedges but in a single region. Using these states, we then show that in this scenario the entanglement never degrades but increases with increasing black hole temperature and holds true no matter how hot the black hole becomes or how small the cosmological constant is. We argue that this phenomenon can have no analogue in the asymptotically flat/anti-de Sitter black hole spacetimes.
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It is shown how the characteristic thermal effects that observers experience in space-times possessing an event horizon can manifest already in a simple quantum system with affine symmetry living on the real line. The derivation presented is essentially group theoretic in nature: a thermal state emerges naturally when comparing different representations of the group of affine transformations of the real line. The freedom in the choice of different notions of translation generators is the key to the Unruh effect on a line we describe.
We consider the dynamics of particles, particularly focusing on circular orbits in the higher-dimensional Majumdar-Papapetrou (MP) spacetimes with two equal mass black holes. It is widely known that in the 5D Schwarzschild-Tangherlini and Myers-Perry backgrounds, there are no stable circular orbits. In contrast, we show that in the 5D MP background, stable circular orbits can always exist when the separation of two black holes is large enough. More precisely, for a large separation, stable circular orbits exist from the vicinity of horizons to infinity; for a medium one, they appear only in a certain finite region bounded by the innermost stable circular orbit and the outermost stable circular orbit outside the horizons; for a small one, they do not appear at all. Moreover, we show that in MP spacetimes in more than 5D, they do not exist for any separations.
We illustrate the analogue of the Unruh effect for a quantum system on the real line. Our derivation relies solely on basic elements of representation theory of the group of affine transformations without a notion of time or metric. Our result shows that a thermal distribution naturally emerges in connecting quantum states belonging to representations associated to distinct notions of translational symmetry.
We discuss the field quantisation of a free massive Dirac fermion in the two causally disconnected static patches of the de Sitter spacetime, by using mode functions that are normalisable on the cosmological event horizon. Using this, we compute the entanglement entropy of the vacuum state corresponding to these two regions, for a given fermionic mode. Further extensions of this result to more general static spherically symmetric and stationary axisymmetric spacetimes are discussed. For the stationary axisymmetric Kerr-de Sitter spacetime in particular, the variations of the entanglement entropy with respect to various eigenvalues and spacetime parameters are depicted numerically. We also comment on such variations when instead we consider the non-extremal black hole event horizon of the same spacetime.
We consider spacetime initiated by a finite-sized boundary on which a pure initial matter state is set as a natural generalization of the Hartle-Hawking no-boundary state. We study entanglement entropy of the gravitationally prepared matter state at the final time slice. We find that the entropy of the initial state or the entanglement island gives the entropy for large subregions on the final time slice. Consequently, we find the entanglement entropy is bounded from above by the boundary area of the island, leading to an entropy bound in terms of the island formula. The island $I$ appears in the analytically continued spacetime, either at the bra or the ket part of the spacetime in Schwinger-Keldysh formalism, and the entropy is given by an average of pseudo entropy of each entanglement island. We find a necessary condition of the initial state to be consistent with the strong sub-additivity. The condition requires that any probe degrees of freedom are thermally entangled with the rest of the system. We then study which initial condition leads to our finite-sized initial boundary or the Hartle-Hawking no-boundary state. Due to the absence of a moment of time reflection symmetry, the island in our setup requires a generalization of the entanglement wedge, which we call {it{pseudo entanglement wedge}}. In pseudo entanglement wedge reconstruction, we consider reconstructing the bulk matter transition matrix on $Acup I$, from a fine-grained state on $A$. The bulk transition matrix is given by a thermofield double state with a projection by the initial state. We provide an AdS/BCFT model, which provides a double holography model of our setup by considering EOW branes with corners. We also find the exponential hardness of such reconstruction task using a generalization of Pythons lunch conjecture to pseudo generalized entropy.
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