13,854 research outputs found
Entanglement renormalization and integral geometry
We revisit the applications of integral geometry in AdS and argue that
the metric of the kinematic space can be realized as the entanglement contour,
which is defined as the additive entanglement density. From the renormalization
of the entanglement contour, we can holographically understand the operations
of disentangler and isometry in multi-scale entanglement renormalization
ansatz. Furthermore, a renormalization group equation of the long-distance
entanglement contour is then derived. We then generalize this integral
geometric construction to higher dimensions and in particular demonstrate how
it works in bulk space of homogeneity and isotropy.Comment: 40 pages, 7 figures. v2: discussions on the general measure added,
typos fixed; v3: sections reorganized, various points clarified, to appear in
JHE
Higher-Derivative Gravity with Non-minimally Coupled Maxwell Field
We construct higher-derivative gravities with a non-minimally coupled Maxwell
field. The Lagrangian consists of polynomial invariants built from the Riemann
tensor and the Maxwell field strength in such a way that the equations of
motion are second order for both the metric and the Maxwell potential. We also
generalize the construction to involve a generic non-minimally coupled -form
field strength. We then focus on one low-lying example in four dimensions and
construct the exact magnetically-charged black holes. We also construct exact
electrically-charged Lifshitz black holes. We obtain approximate dyonic
black holes for the small coupling constant or small charges. We find that the
thermodynamics based on the Wald formalism disagrees with that derived from the
Euclidean action procedure, suggesting this may be a general situation in
higher-derivative gravities with non-minimally coupled form fields. As an
application in the AdS/CFT correspondence, we study the entropy/viscosity ratio
for the AdS or Lifshitz planar black holes, and find that the exact ratio can
be obtained without having to know the details of the solutions, even for this
higher-derivative theory.Comment: Latex, 23 page
Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media
This paper introduces a new discrete fracture model accounting for
non-isothermal compositional multiphase Darcy flows and complex networks of
fractures with intersecting, immersed and non immersed fractures. The so called
hybrid-dimensional model using a 2D model in the fractures coupled with a 3D
model in the matrix is first derived rigorously starting from the
equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully
implicit time integration combined with the Vertex Approximate Gradient (VAG)
finite volume scheme which is adapted to polyhedral meshes and anisotropic
heterogeneous media. The fully coupled systems are assembled and solved in
parallel using the Single Program Multiple Data (SPMD) paradigm with one layer
of ghost cells. This strategy allows for a local assembly of the discrete
systems. An efficient preconditioner is implemented to solve the linear systems
at each time step and each Newton type iteration of the simulation. The
numerical efficiency of our approach is assessed on different meshes, fracture
networks, and physical settings in terms of parallel scalability, nonlinear
convergence and linear convergence
Non-Abelian (Hyperscaling Violating) Lifshitz Black Holes in General Dimensions
We consider Einstein gravities coupled to a cosmological constant and
multiple Yang-Mills fields in general dimensions and find that the
theories admit colored Lifshitz solutions with dynamic exponents . We also
introduce a Maxwell field and construct exact electric charged black holes that
asymptote to the colored Lifshitz spacetimes and analyse their
thermodynamical first law. Furthermore, we introduce a dilaton to the system
and construct Lifshitz spacetimes with hyperscaling violations. After turning
on the Maxwell field, we obtain a class of hyperscaling violating Lifshitz
black holes when .Comment: Latex, 12 pages, a published version in PL
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