7,689 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
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
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
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
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
Spontaneously broken symmetry restoration of quantum fields in the vicinity of neutral and electrically charged black holes
We consider the restoration of a spontaneously broken symmetry of an
interacting quantum scalar field around neutral, i.e., Schwarzschild, and
electrically charged, i.e., Reissner-Nordstr\"om, black holes in four
dimensions. This is done through a semiclassical self-consistent procedure, by
solving the system of non-linear coupled equations describing the dynamics of
the background field and the vacuum polarization. The black hole at its own
horizon generates an indefinitely high temperature which decreases to the
Hawking temperature at infinity. Due to the high temperature in its vicinity,
there forms a bubble around the black hole in which the scalar field can only
assume a value equal to zero, a minimum of energy. Thus, in this region the
symmetry of the energy and the field is preserved. At the bubble radius, there
is a phase transition in the value of the scalar field due to a spontaneous
symmetry breaking mechanism. Indeed, outside the bubble radius the temperature
is low enough such that the scalar field settles with a nonzero value in a new
energy minimum, indicating a breaking of the symmetry in this outer region.
Conversely, there is symmetry restoration from the outer region to the inner
bubble close to the horizon. Specific properties that emerge from different
black hole electric charges are also noteworthy. It is found that colder black
holes, i.e., more charged ones, have a smaller bubble length of restored
symmetry. In the extremal case the bubble has zero length, i.e., there is no
bubble. Additionally, for colder black holes, it becomes harder to excite the
quantum field modes, so the vacuum polarization has smaller values. In the
extremal case, the black hole temperature is zero and the vacuum polarization
is never excited.Comment: 16 pages, 4 figure
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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