7,681 research outputs found
Stationary Black Holes in a Generalized Three-Dimensional Theory of Gravity
We consider a generalized three-dimensional theory of gravity which is
specified by two fields, the graviton and the dilaton, and one parameter. This
theory contains, as particular cases, three-dimensional General Relativity and
three-dimensional String Theory. Stationary black hole solutions are generated
from the static ones using a simple coordinate transformation. The stationary
black holes solutions thus obtained are locally equivalent to the corresponding
static ones, but globally distinct. The mass and angular momentum of the
stationary black hole solutions are computed using an extension of the Regge
and Teitelboim formalism. The causal structure of the black holes is described.Comment: 12 pages, Late
Conformal entropy from horizon states: Solodukhin's method for spherical, toroidal, and hyperbolic black holes in D-dimensional anti-de Sitter spacetimes
A calculation of the entropy of static, electrically charged, black holes
with spherical, toroidal, and hyperbolic compact and oriented horizons, in D
spacetime dimensions, is performed. These black holes live in an anti-de Sitter
spacetime, i.e., a spacetime with negative cosmological constant. To find the
entropy, the approach developed by Solodukhin is followed. The method consists
in a redefinition of the variables in the metric, by considering the radial
coordinate as a scalar field. Then one performs a 2+(D-2) dimensional
reduction, where the (D-2) dimensions are in the angular coordinates, obtaining
a 2-dimensional effective scalar field theory. This theory is a conformal
theory in an infinitesimally small vicinity of the horizon. The corresponding
conformal symmetry will then have conserved charges, associated with its
infinitesimal conformal generators, which will generate a classical Poisson
algebra of the Virasoro type. Shifting the charges and replacing Poisson
brackets by commutators, one recovers the usual form of the Virasoro algebra,
obtaining thus the level zero conserved charge eigenvalue L_0, and a nonzero
central charge c. The entropy is then obtained via the Cardy formula.Comment: 21 page
The Two-Dimensional Analogue of General Relativity
General Relativity in three or more dimensions can be obtained by taking the
limit in the Brans-Dicke theory. In two dimensions
General Relativity is an unacceptable theory. We show that the two-dimensional
closest analogue of General Relativity is a theory that also arises in the
limit of the two-dimensional Brans-Dicke theory.Comment: 8 pages, LaTeX, preprint DF/IST-17.9
Alignment of velocity fields for video surveillance
Velocity fields play an important role in surveillance since they describe typical motion behaviors of video objects (e.g., pedestrians) in the scene. This paper presents an algorithm for the alignment of velocity fields acquired by different cameras, at different time intervals, from different viewpoints. Velocity fields are aligned using a warping function which maps corresponding points and vectors in both fields. The warping parameters are estimated by minimizing a non-linear least squares energy. Experimental tests show that the proposed model is able to compensate significant misalignments, including translation, rotation and scaling
Collapsing shells of radiation in anti-de Sitter spacetimes and the hoop and cosmic censorship conjectures
Gravitational collapse of radiation in an anti-de Sitter background is
studied. For the spherical case, the collapse proceeds in much the same way as
in the Minkowski background, i.e., massless naked singularities may form for a
highly inhomogeneous collapse, violating the cosmic censorship, but not the
hoop conjecture. The toroidal, cylindrical and planar collapses can be treated
together. In these cases no naked singularity ever forms, in accordance with
the cosmic censorship. However, since the collapse proceeds to form toroidal,
cylindrical or planar black holes, the hoop conjecture in an anti-de Sitter
spacetime is violated.Comment: 4 pages, Revtex Journal: to appear in Physical Review
BLACK HOLES IN THREE-DIMENSIONAL DILATON GRAVITY THEORIES
Three dimensional black holes in a generalized dilaton gravity action theory
are analysed. The theory is specified by two fields, the dilaton and the
graviton, and two parameters, the cosmological constant and the Brans-Dicke
parameter. It contains seven different cases, of which one distinguishes as
special cases, string theory, general relativity and a theory equivalent to
four dimensional general relativity with one Killing vector. We study the
causal structure and geodesic motion of null and timelike particles in the
black hole geometries and find the ADM masses of the different solutions.Comment: 19 pages, latex, 4 figures as uuencoded postscript file
The Three-Dimensional BTZ Black Hole as a Cylindrical System in Four-Dimensional General Relativity
It is shown how to transform the three dimensional BTZ black hole into a four
dimensional cylindrical black hole (i.e., black string) in general relativity.
This process is identical to the transformation of a point particle in three
dimensions into a straight cosmic string in four dimensions.Comment: Latex, 9 page
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