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Register a new userDirac fermion, cosmological event horizons and quantum entanglement
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Added by
Sourav Bhattacharya
Publication date
2019
fields
Physics
and research's language is
English
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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.
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We propose a holographic map between Einstein gravity coupled to matter in a de Sitter background and large N quantum mechanics of a system of spins. Holography maps a spin model with a finite dimensional Hilbert space defined on a version of the stretched horizon into bulk gravitational dynamics. The full Hamiltonian of the spin model contains a non-local piece which generates chaotic dynamics, widely conjectured to be a necessary part of quantum gravity, and a local piece which recovers the perturbative spectrum in the bulk.
We consider massless fields of arbitrary spin in de Sitter space. We introduce a spinor-helicity formalism, which encodes the field data on a cosmological horizon. These variables reduce the free S-matrix in an observers causal patch, i.e. the evolution of free fields from one horizon to another, to a simple Fourier transform. We show how this result arises via twistor theory, by decomposing the horizon<->horizon problem into a pair of (more symmetric) horizon<->twistor problems.
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.
In this note we present preliminary study on the relation between the quantum entanglement of boundary states and the quantum geometry in the bulk in the framework of spin networks. We conjecture that the emergence of space with non-zero volume reflects the non-perfectness of the $SU(2)$-invariant tensors. Specifically, we consider four-valent vertex with identical spins in spin networks. It turns out that when $j = 1/2$ and $j = 1$, the maximally entangled $SU(2)$-invariant tensors on the boundary correspond to the eigenstates of the volume square operator in the bulk, which indicates that the quantum geometry of tetrahedron has a definite orientation.
We argue that classical $(alpha)$ effects qualitatively modify the structure of Euclidean black hole horizons in string theory. While low energy modes experience the geometry familiar from general relativity, high energy ones see a rather different geometry, in which the Euclidean horizon can be penetrated by an amount that grows with the radial momentum of the probe. We discuss this in the exactly solvable SL(2,R)/U(1) black hole, where it is a manifestation of the black hole/Sine-Liouville duality.
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