21 research outputs found
On noncommutative spherically symmetric spaces
Two families of noncommutative extensions are given of a general space-time
metric with spherical symmetry, both based on the matrix truncation of the
functions on the sphere of symmetry. The first family uses the truncation to
foliate space as an infinite set of spheres, is of dimension four and
necessarily time-dependent; the second can be time-dependent or static, is of
dimension five and uses the truncation to foliate the internal space.Comment: 22 page
Noncommutative de Sitter and FRW spaces
Several versions of fuzzy four-dimensional de Sitter space are constructed
using the noncommutative frame formalism. Although all noncommutative
spacetimes which are found have commutative de Sitter metric as a classical
limit, the algebras and the differential calculi which define them have many
differences which we derive and discuss.Comment: 20 page
The fuzzy BTZ
We introduce a model of a noncommutative BTZ black hole, obtained by
quantisation of Poincar\'e coordinates together with a moving frame. The fuzzy
BTZ black hole carries a covariant differential calculus, satisfies Einstein's
equations and has a constant negative curvature. The construction passes
through a larger space, the fuzzy anti-de Sitter, and implements discrete BTZ
identifications as conjugations by a unitary operator. We derive the spectrum
of the suitably regularised radial coordinate: it consists of a continuum of
scattering states outside the horizon and an infinite discrete set of
bound states inside
WKB Approximation in Noncommutative Gravity
We consider the quasi-commutative approximation to a noncommutative geometry
defined as a generalization of the moving frame formalism. The relation which
exists between noncommutativity and geometry is used to study the properties of
the high-frequency waves on the flat background.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA