scholarly journals Anti–de Sitter–CFT correspondence in three-dimensional supergravity

1998 ◽  
Vol 58 (8) ◽  
Author(s):  
Máximo Bañados ◽  
Karin Bautier ◽  
Olivier Coussaert ◽  
Marc Henneaux ◽  
Miguel Ortiz
Keyword(s):  
Three Dimensional ◽  
De Sitter

scholarly journals Spherical and planar three-dimensional anti-de Sitter black holes

2004 ◽  
Vol 21 (4) ◽  
pp. 875-897 ◽  
Author(s):  
Vilson T Zanchin ◽  
Alex S Miranda
Keyword(s):  
Black Holes ◽  
Three Dimensional ◽  
De Sitter

scholarly journals AdS3 GRAVITATIONAL INSTANTONS FROM CONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (28) ◽  
pp. 1961-1981 ◽  
Author(s):  
SHUHEI MANO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bound States ◽  
Three Dimensional ◽  
Partition Functions ◽  
De Sitter ◽  
Btz Black Hole ◽  
Gravitational Instantons ◽  
Conformal Field ◽  
Horizon Geometry

A conformal field theory on the boundary of three-dimensional asymptotic anti-de Sitter spaces which appear as near horizon geometry of D-brane bound states is discussed. It is shown that partition functions of gravitational instantons appear as high and low temperature limits of the partition function of the conformal field theory. The result reproduces phase transition between the anti-de Sitter space and the BTZ black hole in the bulk gravity.

scholarly journals Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1867
Author(s):  
Alexander Breev ◽  
Alexander Shapovalov
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Homogeneous Space ◽  
Integration Method ◽  
Homogeneous Spaces ◽  
Separation Of Variables ◽  
General Structure ◽  
Three Dimensional ◽  
De Sitter ◽  
Elementary Functions

We develop a non-commutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space. This allows us to effectively apply the non-commutative integration method of linear partial differential equations on Lie groups. This method differs from the well-known method of separation of variables and to some extent can often supplement it. The general structure of the method developed is illustrated with an example of a homogeneous space which does not admit separation of variables in the Dirac equation. However, the basis of exact solutions to the Dirac equation is constructed explicitly by the non-commutative integration method. In addition, we construct a complete set of new exact solutions to the Dirac equation in the three-dimensional de Sitter space-time AdS3 using the method developed. The solutions obtained are found in terms of elementary functions, which is characteristic of the non-commutative integration method.

scholarly journals Phase Transition at the Metric Elastic Universe

1996 ◽  
Vol 168 ◽  
pp. 569-570
Author(s):  
Alexander Gusev
Keyword(s):  
Phase Transition ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Vacuum State ◽  
Space Time ◽  
Deformation Tensor ◽  
De Sitter ◽  
Initial State ◽  
Deformation State ◽  
The Universe

At the last time the concept of the curved space-time as the some medium with stress tensor σαβon the right part of Einstein equation is extensively studied in the frame of the Sakharov - Wheeler metric elasticity(Sakharov (1967), Wheeler (1970)). The physical cosmology pre- dicts a different phase transitions (Linde (1990), Guth (1991)). In the frame of Relativistic Theory of Finite Deformations (RTFD) (Gusev (1986)) the transition from the initial stateof the Universe (Minkowskian's vacuum, quasi-vacuum(Gliner (1965), Zel'dovich (1968)) to the final stateof the Universe(Friedmann space, de Sitter space) has the form of phase transition(Gusev (1989) which is connected with different space-time symmetry of the initial and final states of Universe(from the point of view of isometric groupGnof space). In the RTFD (Gusev (1983), Gusev (1989)) the space-time is described by deformation tensorof the three-dimensional surfaces, and the Einstein's equations are viewed as the constitutive relations between the deformations ∊αβand stresses σαβ. The vacuum state of Universe have the visible zero physical characteristics and one is unsteady relatively quantum and topological deformations (Gunzig & Nardone (1989), Guth (1991)). Deformations of vacuum state, identifying with empty Mikowskian's space are described the deformations tensor ∊αβ, wherethe metrical tensor of deformation state of 3-geometry on the hypersurface, which is ortogonaled to the four-velocityis the 3 -geometry of initial state,is a projection tensor.

UPPER AND LOWER BOUNDS FOR THE VOLUME OF A COMPACT SPACELIKE HYPERSURFACE IN A GENERALIZED ROBERTSON–WALKER SPACETIME

2013 ◽  
Vol 11 (01) ◽  
pp. 1450006 ◽  
Author(s):  
JUAN ÁNGEL ALEDO ◽  
ALFONSO ROMERO ◽  
RAFAEL M. RUBIO
Keyword(s):  
Lower Bounds ◽  
Three Dimensional ◽  
Spacelike Hypersurface ◽  
Upper And Lower Bounds ◽  
Warping Function ◽  
First Eigenvalue ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Angle Function ◽  
Spacelike Hypersurfaces

We provide upper and lower bounds for the volume of a compact spacelike hypersurface in an (n + 1)-dimensional Generalized Robertson–Walker (GRW) spacetime in terms of the volume of the fiber, the hyperbolic angle function and the warping function. Under several geometrical and physical assumptions, we characterize the spacelike slices as the only spacelike hypersurfaces where these bounds are attained. As a consequence of these results, we get an upper bound for the first eigenvalue of a compact spacelike surface in a three-dimensional GRW spacetime whose fiber is a topological sphere, which includes the case of the three-dimensional De Sitter spacetime, and show that the bound is attained if and only if M is a spacelike slice.

Energy loss of a heavy particle near a three-dimensional charged hairy black hole

2014 ◽  
Vol 92 (11) ◽  
pp. 1481-1484 ◽  
Author(s):  
J. Naji ◽  
S. Heydari ◽  
A. Amjadi
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Energy Loss ◽  
Heavy Particle ◽  
Three Dimensional ◽  
Three Dimensions ◽  
De Sitter ◽  
Conformal Field ◽  
Scalar Charge ◽  
Hairy Black Hole

In this paper, we consider a charged black hole in three dimensions with a scalar charge and discuss energy loss of a heavy particle moving near the black hole horizon. This analysis is useful when anti-de Sitter space – conformal field theory correspondence is applied. We find that an electric charge of a black hole increases the drag force but a scalar charge decreases it.

scholarly journals GEOMETRIC MODULAR ACTION AND SPACETIME SYMMETRY GROUPS

2000 ◽  
Vol 12 (04) ◽  
pp. 475-560 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
OLAF DREYER ◽  
MARTIN FLORIG ◽  
STEPHEN J. SUMMERS
Keyword(s):  
Isometry Group ◽  
Three Dimensional ◽  
Algebraic Characterization ◽  
Symmetry Groups ◽  
De Sitter ◽  
Vacuum States ◽  
Point Transformations ◽  
Projective Representations ◽  
Modular Covariance

A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable additional conditions, these groups induce groups of point transformations on these space-times, which may be interpreted as symmetry groups. The consequences of this condition are studied in detail in application to two concrete space-times — four-dimensional Minkowski and three-dimensional de Sitter spaces — for which it is shown how this condition characterizes the states invariant under the respective isometry group. An intriguing new algebraic characterization of vacuum states is given. In addition, the logical relations between the condition proposed in this paper and the condition of modular covariance, widely used in the literature, are completely illuminated.

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