4,254 research outputs found
Lattice Universes in 2+1-dimensional gravity
Lattice universes are spatially closed space-times of spherical topology in
the large, containing masses or black holes arranged in the symmetry of a
regular polygon or polytope. Exact solutions for such spacetimes are found in
2+1 dimensions for Einstein gravity with a non-positive cosmological constant.
By means of a mapping that preserves the essential nature of geodesics we
establish analogies between the flat and the negative curvature cases. This map
also allows treatment of point particles and black holes on a similar footing.Comment: 14 pages 7 figures, to appear in Festschrift for Vince Moncrief (CQG
Collapse of Kaluza-Klein Bubbles
Kaluza-Klein theory admits ``bubble" configurations, in which the
circumference of the fifth dimension shrinks to zero on some compact surface. A
three parameter family of such bubble initial data at a moment of time-symmetry
(some including a magnetic field) has been found by Brill and Horowitz,
generalizing the (zero-energy) ``Witten bubble" solution. Some of these data
have negative total energy. We show here that all the negative energy bubble
solutions start out expanding away from the moment of time symmetry, while the
positive energy bubbles can start out either expanding or contracting. Thus it
is unlikely that the negative energy bubbles would collapse and produce a naked
singularity.Comment: 6 pages, plain LaTeX, UMDGR-94-08
Reversibility Checking for Markov Chains
In this paper, we present reversibility preserving operations on Markov chain
transition matrices. Simple row and column operations allow us to create new
reversible transition matrices and yield an easy method for checking a Markov
chain for reversibility
Integrability of the N-body problem in (2+1)-AdS gravity
We derive a first order formalism for solving the scattering of point sources
in (2+1) gravity with negative cosmological constant. We show that their
physical motion can be mapped, with a polydromic coordinate transformation, to
a trivial motion, in such a way that the point sources move as time-like
geodesics (in the case of particles) or as space-like geodesics (in the case of
BTZ black holes) of a three-dimensional hypersurface immersed in a
four-dimensional Minkowskian space-time, and that the two-body dynamics is
solved by two invariant masses, whose difference is simply related to the total
angular momentum of the system.Comment: 15 pages, LaTeX, no figure
Siri, Alexa, and Other Digital Assistants: A Study of Customer Satisfaction With Artificial Intelligence Applications
Siri, Alexa, and other digital assistants are rapidly becoming embraced by consumers and the adoption is projected to grow from 390 million to 1.8 billion for the period of 2015 to 2021. Digital assistants are offering benefits to consumers while also proving to be a disruptive technology for businesses. Coupling digital assistants with other artificial intelligence technologies offers the potential to transform companies by creating more efficient business processes, automating complex tasks, and improving the customer service experience. Businesses have begun integrating this technology into their operations with the expectation of achieving significant productivity gains. Customer satisfaction has been discussed extensively throughout marketing literature. Yet, there is little empirical evidence of customer satisfaction with digital assistants. This study used PLS-SEM to analyze 244 survey responses obtained from a cross-section of consumers. Using the Expectations Confirmation Theory as its foundation, the study identified that expectations and confirmation of expectations substantially explained customer satisfaction with digital assistants. For practice, the study provides guidance which allows firms to prioritize marketing and managerial activities. Firms should focus priorities on assisting digital assistant users to become aware of new skill capabilities while also providing relevant examples of how these skills can be used to meet user needs. In addition, priorities should be focused on assisting users with understanding how the average person can use digital assistants to perform more than just mundane tasks with relative ease. These priorities were identified as areas of high importance for customer satisfaction and require performance improvements
Uniqueness of the asymptotic AdS3 geometry
We explicitly show that in (2+1) dimensions the general solution of the
Einstein equations with negative cosmological constant on a neigbourhood of
timelike spatial infinity can be obtained from BTZ metrics by coordinate
transformations corresponding geometrically to deformations of their spatial
infinity surface. Thus, whatever the topology and geometry of the bulk, the
metric on the timelike extremities is BTZ.Comment: LaTeX, 8 pages, no figures, version that will appear in Class. Quant.
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Perturbative Analysis of the Two-body Problem in (2+1)-AdS gravity
We derive a perturbative scheme to treat the interaction between point
sources and AdS-gravity. The interaction problem is equivalent to the search of
a polydromic mapping , endowed with 0(2,2) monodromies,
between the physical coordinate system and a Minkowskian 4-dimensional
coordinate system, which is however constrained to live on a hypersurface. The
physical motion of point sources is therefore mapped to a geodesic motion on
this hypersuface. We impose an instantaneous gauge which induces a set of
equations defining such a polydromic mapping. Their consistency leads naturally
to the Einstein equations in the same gauge. We explore the restriction of the
monodromy group to O(2,1), and we obtain the solution of the fields
perturbatively in the cosmological constant.Comment: 19 pages, no figures, LaTeX fil
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