951 research outputs found
A holographic proof of the strong subadditivity of entanglement entropy
When a quantum system is divided into subsystems, their entanglement
entropies are subject to an inequality known as "strong subadditivity". For a
field theory this inequality can be stated as follows: given any two regions of
space and , . Recently, a
method has been found for computing entanglement entropies in any field theory
for which there is a holographically dual gravity theory. In this note we give
a simple geometrical proof of strong subadditivity employing this holographic
prescription.Comment: 9 pages, 3 figure
Strong subadditivity and the covariant holographic entanglement entropy formula
Headrick and Takayanagi showed that the Ryu-Takayanagi holographic
entanglement entropy formula generally obeys the strong subadditivity (SSA)
inequality, a fundamental property of entropy. However, the Ryu-Takayanagi
formula only applies when the bulk spacetime is static. It is not known whether
the covariant generalization proposed by Hubeny, Rangamani, and Takayanagi
(HRT) also obeys SSA. We investigate this question in three-dimensional
AdS-Vaidya spacetimes, finding that SSA is obeyed as long as the bulk spacetime
satisfies the null energy condition. This provides strong support for the
validity of the HRT formula.Comment: 38 page
Interfacial Studies in Semiconductor Heterostructures by X-Ray Diffraction Techniques
X-ray radiation is a non-destructive probe well suited to assess structural perfection of semiconductor material. Three techniques are used to study the interfacial roughness, period fluctuations and annealing-induced interdiffusion in various superlattice structures. Reflectivity of long period Si/Si1-xGex multiple quantum wells reveals an asymmetry oriented along the direction of miscut in the interface roughness with the Si1-xGex to Si interfaces being about twice as rough (0.5 versus 0.3 nm) as the Si to Si1-xGex interfaces. For Si-Si0.65Ge0.35 multiple quantum wells, diffuse scattering is minimal for a growth temperature of 550°C and increases substantially at very low (250°C) or high (750°C) growth temperatures. In (SimGen)p short period superlattices, the X-ray reflectivity data are consistent with interfacial mixing over about two monolayers and thickness fluctuations of about 5% vertically in the structures. For superlattices grown on vicinal surfaces, the roughness spectrum is correlated with the surface miscut orientation. Double-crystal X-ray diffraction using symmetrical and asymmetrical reflections has been used to study epitaxial lattice distortion and strain relaxation in InGaAs/GaAs heterostructures grown on (100) on-orientation and 2° off (100) GaAs surfaces. It is shown that thick InGaAs films retain an appreciable fraction of their initial strain and that their crystal lattice is triclinically distorted. The magnitude of the deformation is larger when growth is carried out on a vicinal surface
A numerical approach to finding general stationary vacuum black holes
The Harmonic Einstein equation is the vacuum Einstein equation supplemented
by a gauge fixing term which we take to be that of DeTurck. For static black
holes analytically continued to Riemannian manifolds without boundary at the
horizon this equation has previously been shown to be elliptic, and Ricci flow
and Newton's method provide good numerical algorithms to solve it. Here we
extend these techniques to the arbitrary cohomogeneity stationary case which
must be treated in Lorentzian signature. For stationary spacetimes with
globally timelike Killing vector the Harmonic Einstein equation is elliptic. In
the presence of horizons and ergo-regions it is less obviously so. Motivated by
the Rigidity theorem we study a class of stationary black hole spacetimes,
considered previously by Harmark, general enough to include the asymptotically
flat case in higher dimensions. We argue the Harmonic Einstein equation
consistently truncates to this class of spacetimes giving an elliptic problem.
The Killing horizons and axes of rotational symmetry are boundaries for this
problem and we determine boundary conditions there. As a simple example we
numerically construct 4D rotating black holes in a cavity using Anderson's
boundary conditions. We demonstrate both Newton's method and Ricci flow to find
these Lorentzian solutions.Comment: 43 pages, 7 figure
Tachyon Condensation with B-field
We discuss classical solutions of a graviton-dilaton-B_{\mu\nu}-tachyon
system. Both constant tachyon solutions, including AdS_3 solutions, and
space-dependent tachyon solutions are investigated, and their possible
implications to closed string tachyon condensation are argued. The stability
issue of the AdS_3 solutions is also discussed.Comment: 10 pages, references adde
Ricci flow and black holes
Gradient flow in a potential energy (or Euclidean action) landscape provides
a natural set of paths connecting different saddle points. We apply this method
to General Relativity, where gradient flow is Ricci flow, and focus on the
example of 4-dimensional Euclidean gravity with boundary S^1 x S^2,
representing the canonical ensemble for gravity in a box. At high temperature
the action has three saddle points: hot flat space and a large and small black
hole. Adding a time direction, these also give static 5-dimensional
Kaluza-Klein solutions, whose potential energy equals the 4-dimensional action.
The small black hole has a Gross-Perry-Yaffe-type negative mode, and is
therefore unstable under Ricci flow. We numerically simulate the two flows
seeded by this mode, finding that they lead to the large black hole and to hot
flat space respectively, in the latter case via a topology-changing
singularity. In the context of string theory these flows are world-sheet
renormalization group trajectories. We also use them to construct a novel free
energy diagram for the canonical ensemble.Comment: 31 pages, 14 color figures. v2: Discussion of the metric on the space
of metrics corrected and expanded, references adde
The Simplicial Ricci Tensor
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of
gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the
moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the
Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton
to define a non-linear, diffusive Ricci flow (RF) that was fundamental to
Perelman's proof of the Poincare conjecture. Analytic applications of RF can be
found in many fields including general relativity and mathematics. Numerically
it has been applied broadly to communication networks, medical physics,
computer design and more. In this paper, we use Regge calculus (RC) to provide
the first geometric discretization of the Ric. This result is fundamental for
higher-dimensional generalizations of discrete RF. We construct this tensor on
both the simplicial lattice and its dual and prove their equivalence. We show
that the Ric is an edge-based weighted average of deficit divided by an
edge-based weighted average of dual area -- an expression similar to the
vertex-based weighted average of the scalar curvature reported recently. We use
this Ric in a third and independent geometric derivation of the RC Einstein
tensor in arbitrary dimension.Comment: 19 pages, 2 figure
Gott time machines in the Anti-de Sitter space
In 1991 Gott presented a solution of Einstein's field equations in 2+1
dimensions with that contained closed timelike curves (CTC's).
This solution was remarkable because at first it did not seem to be unphysical
in any other respect. Later, however, it was shown that Gott's solution is
tachyonic in a certain sense. Here the case is discussed. We show
that it is possible to construct CTC's also in this case, in a way analogous to
that used by Gott. We also show that this construction still is tachyonic.
means that we are dealing with Anti-de Sitter space, and since
the CTC-construction necessitates some understanding of its structure, a few
pages are devoted to this subject.Comment: 11 page
Topologically Massive Gravity and Ricci-Cotton Flow
We consider Topologically Massive Gravity (TMG), which is three dimensional
general relativity with a cosmological constant and a gravitational
Chern-Simons term. When the cosmological constant is negative the theory has
two potential vacuum solutions: Anti-de Sitter space and Warped Anti-de Sitter
space. The theory also contains a massive graviton state which renders these
solutions unstable for certain values of the parameters and boundary
conditions. We study the decay of these solutions due to the condensation of
the massive graviton mode using Ricci-Cotton flow, which is the appropriate
generalization of Ricci flow to TMG. When the Chern-Simons coupling is small
the AdS solution flows to warped AdS by the condensation of the massive
graviton mode. When the coupling is large the situation is reversed, and warped
AdS flows to AdS. Minisuperspace models are constructed where these flows are
studied explicitly
- …