194 research outputs found
Entwinement and the emergence of spacetime
It is conventional to study the entanglement between spatial regions of a
quantum field theory. However, in some systems entanglement can be dominated by
"internal", possibly gauged, degrees of freedom that are not spatially
organized, and that can give rise to gaps smaller than the inverse size of the
system. In a holographic context, such small gaps are associated to the
appearance of horizons and singularities in the dual spacetime. Here, we
propose a concept of entwinement, which is intended to capture this fine
structure of the wavefunction. Holographically, entwinement probes the
entanglement shadow -- the region of spacetime not probed by the minimal
surfaces that compute spatial entanglement in the dual field theory. We
consider the simplest example of this scenario -- a 2d conformal field theory
(CFT) that is dual to a conical defect in AdS3 space. Following our previous
work, we show that spatial entanglement in the CFT reproduces spacetime
geometry up to a finite distance from the conical defect. We then show that the
interior geometry up to the defect can be reconstructed from entwinement that
is sensitive to the discretely gauged, fractionated degrees of freedom of the
CFT. Entwinement in the CFT is related to non-minimal geodesics in the conical
defect geometry, suggesting a potential quantum information theoretic meaning
for these objects in a holographic context. These results may be relevant for
the reconstruction of black hole interiors from a dual field theory.Comment: v2: Sec. 4.3 amende
From quantum to classical instability in relativistic stars
It has been shown that gravitational fields produced by realistic
classical-matter distributions can force quantum vacuum fluctuations of some
nonminimally coupled free scalar fields to undergo a phase of exponential
growth. The consequences of this unstable phase to the background spacetime
have not been addressed so far due to known difficulties concerning
backreaction in semiclassical gravity. It seems reasonable to believe, however,
that the quantum fluctuations will "classicalize" when they become large
enough, after which backreaction can be treated in the general-relativistic
context. Here we investigate the emergence of a classical regime out of the
quantum field evolution during the unstable phase. By studying the appearance
of classical correlations and loss of quantum coherence, we show that by the
time backreaction becomes important the system already behaves classically.
Consequently, the gravity-induced instability leads naturally to initial
conditions for the eventual classical description of the backreaction. Our
results give support to previous analyses which treat classically the
instability of scalar fields in the spacetime of relativistic stars, regardless
whether the instability is triggered by classical or quantum perturbations.Comment: 16 pages. Minor changes to match the published versio
Generalized curvature-matter couplings in modified gravity
In this work, we review a plethora of modified theories of gravity with
generalized curvature-matter couplings. The explicit nonminimal couplings, for
instance, between an arbitrary function of the scalar curvature and the
Lagrangian density of matter, induces a non-vanishing covariant derivative of
the energy-momentum tensor, implying non-geodesic motion and consequently leads
to the appearance of an extra force. Applied to the cosmological context, these
curvature-matter couplings lead to interesting phenomenology, where one can
obtain a unified description of the cosmological epochs. We also consider the
possibility that the behavior of the galactic flat rotation curves can be
explained in the framework of the curvature-matter coupling models, where the
extra-terms in the gravitational field equations modify the equations of motion
of test particles, and induce a supplementary gravitational interaction. In
addition to this, these models are extremely useful for describing dark
energy-dark matter interactions, and for explaining the late-time cosmic
acceleration.Comment: 55 pages, to appear as a review paper in a Special Issue of Galaxies:
"Beyond Standard Gravity and Cosmology". V2: minor corrections and references
added. Matches published versio
Cartan geometry of spacetimes with a nonconstant cosmological function
We present the geometry of spacetimes that are tangentially approximated by
de Sitter spaces whose cosmological constants vary over spacetime. Cartan
geometry provides one with the tools to describe manifolds that reduce to a
homogeneous Klein space at the infinitesimal level. We consider a Cartan
geometry in which the underlying Klein space is at each point a de Sitter
space, for which the combined set of pseudo-radii forms a nonconstant function
on spacetime. We show that the torsion of such a geometry receives a
contribution that is not present for a cosmological constant. The structure
group of the obtained de Sitter-Cartan geometry is by construction the Lorentz
group . Invoking the theory of nonlinear realizations, we extend the
class of symmetries to the enclosing de Sitter group , and compute the
corresponding spin connection, vierbein, curvature, and torsion.Comment: 6 pages. Matches version to be published in Physical Review D;
section reviewing Cartan geometry removed, references adde
Noninertial effects on a Dirac neutral particle inducing an analogue of the Landau quantization in the cosmic string spacetime
We discuss the behaviour of external fields that interact with a Dirac
neutral particle with a permanent electric dipole moment in order to achieve
relativistic bound states solutions in a noninertial frame and in the presence
of a topological defect spacetime. We show that the noninertial effects of the
Fermi-Walker reference frame induce a radial magnetic field even in the absence
of magnetic charges, which is influenced by the topology of the cosmic string
spacetime. We then discuss the conditions that the induced fields must satisfy
to yield the relativistic bound states corresponding to the
Landau-He-McKellar-Wilkens quantization in the cosmic string spacetime. Finally
we obtain the Dirac spinors for positive-energy solutions and the Gordon
decomposition of the Dirac probability current.Comment: 15 pages, no figure, this paper will be published in volume 42 of the
Brazilian Journal of Physic
Vacuum entanglement and black hole entropy of gauge fields
Black holes in general relativity carry an entropy whose value is given by the Bekenstein-Hawking formula, but whose statistical origin remains obscure. Such horizons also possess an entanglement entropy, which has a clear statistical meaning but no a priori relation to the dynamics of gravity. For free minimally-coupled scalar and spinor fields, these two quantities are intimately related: the entanglement entropy is the one-loop correction to the black hole entropy due to renormalization of Newton's constant. For gauge fields, the entanglement entropy and the one-loop correction to the black hole entropy differ. This dissertation addresses two issues concerning the entanglement entropy of gauge fields, and its relation black hole entropy.
First, for abelian gauge fields Kabat identified a negative divergent contribution to the black hole entropy that is not part of the entanglement entropy, known as a ``contact term''. We show that the contact term can be attributed to an ambiguous expression for the gauge field's contribution to the Wald entropy. Moreover, in two-dimensional de Sitter space, the contact term arises from an incorrect treatment of zero modes and is therefore unphysical. In a manifestly gauge-invariant reduced phase space quantization of two-dimensional gauge theory, the gauge field contribution to the entropy is positive, finite, and equal to the entanglement entropy. This suggests that the contact term in more than two dimensions may also be unphysical.
Second, we consider lattice gauge theory and point out that the Hilbert space corresponding to a region of space includes edge states that transform nontrivially under gauge transformations. By decomposing these edge states in irreducible representations of the gauge group, the entanglement entropy of an arbitrary state is shown to be a sum of a bulk entropy and a boundary entropy associated to the edge states. This entropy formula agrees with the two-dimensional results from the reduced phase space quantization. These results are applied to several examples, including the ground state in the strong coupling expansion of Kogut and Susskind, and the entropy of the edge states is found to be the dominant contribution to the entanglement entropy
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