scholarly journals The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry

2017 ◽  
Vol 4 (1) ◽  
pp. 183-199 ◽  
Author(s):  
Andrea Seppi
Keyword(s):  
Negative Curvature ◽  
Three Dimensional ◽  
De Sitter Space ◽  
Spacelike Surface ◽  
De Sitter ◽  
Algebraic Construction ◽  
Hyperbolic Metrics ◽  
Genus 2 ◽  
Flux Homomorphism ◽  
Closed Oriented Surface

Abstract Given a smooth spacelike surface ∑ of negative curvature in Anti-de Sitter space of dimension 3, invariant by a representation p: π1 (S) → PSL2ℝ x PSL2ℝ where S is a closed oriented surface of genus ≥ 2, a canonical construction associates to ∑ a diffeomorphism φ∑ of S. It turns out that φ∑ is a symplectomorphism for the area forms of the two hyperbolic metrics h and h' on S induced by the action of p on ℍ2 x ℍ2. Using an algebraic construction related to the flux homomorphism, we give a new proof of the fact that φ∑ is the composition of a Hamiltonian symplectomorphism of (S, h) and the unique minimal Lagrangian diffeomorphism from (S, h) to (S, h’).

scholarly journals Constant angle spacelike surface in de Sitter space S₁³

2017 ◽  
Vol 35 (3) ◽  
pp. 79-93
Author(s):  
Tugba Mert ◽  
Baki Karlıga
Keyword(s):  
Vector Field ◽  
De Sitter Space ◽  
Normal Vector ◽  
Spacelike Surface ◽  
De Sitter ◽  
Unit Normal Vector ◽  
Normal Vector Field ◽  
Constant Angle ◽  
Unit Normal Vector Field ◽  
Unit Normal

In this paper; using the angle between unit normal vector field of surfaces and a fixed spacelike axis in R₁⁴, we develop two class of spacelike surface which are called constant timelike angle surfaces with timelike and spacelike axis in de Sitter space S₁³.

scholarly journals The central charge in three-dimensional anti-de Sitter space

1999 ◽  
Vol 16 (6) ◽  
pp. 1733-1736 ◽  
Author(s):  
Maximo Bañados ◽  
Miguel E Ortiz
Keyword(s):  
Central Charge ◽  
Three Dimensional ◽  
De Sitter Space ◽  
De Sitter

scholarly journals Complete maximal spacelike surfaces in an anti-de Sitter space {\bf H}^{4}_{2}(c)

2000 ◽  
Vol 42 (1) ◽  
pp. 139-156
Author(s):  
Qing-Ming Cheng
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
De Sitter Space ◽  
Second Fundamental Form ◽  
Spacelike Surface ◽  
De Sitter ◽  
Totally Geodesic ◽  
The Second Fundamental Form ◽  
Spacelike Surfaces ◽  
Hyperbolic Cylinder

In this paper, we prove that if M^2 is a complete maximal spacelike surface of an anti-de Sitter space {\bf H}^{4}_{2}(c) with constant scalar curvature, then S=0, S={-10c\over 11}, S={-4c\over 3} or S=-2c, where S is the squared norm of the second fundamental form of M^{2}. Also(1) S=0 if and only if M^2 is the totally geodesic surface {\bf H}^2(c);(2) S={-4c\over 3} if and only if M^2 is the hyperbolic Veronese surface;(3) S=-2c if and only if M^2 is the hyperbolic cylinder of the totally geodesicsurface {\bf H}^{3}_{1}(c) of {\bf H}^{4}_{2}(c).1991 Mathematics Subject Classifaction 53C40, 53C42.

scholarly journals STRINGS IN AdS3 AND THE SL(2, R) WZW MODEL

2001 ◽  
Vol 16 (05) ◽  
pp. 677-682
Author(s):  
HIROSI OOGURI
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Partition Function ◽  
Long Strings ◽  
Three Dimensional ◽  
De Sitter Space ◽  
De Sitter ◽  
Btz Black Hole ◽  
Discrete States ◽  
The One

Strings in the three-dimensional anti-de Sitter space in the NS background is described by the SL(2, R) WZW model. We present a complete description of the Hilbert space of the model. We then compute the one-loop partition function for Euclidean BTZ black hole backgrounds or equivalently thermal AdS3 backgrounds which are quotients of Euclidean AdS3. We see long strings and discrete states in agreement with the structure of the Hilbert space.

scholarly journals ENTROPY OF THE THREE-DIMENSIONAL SCHWARZSCHILD–de SITTER BLACK HOLE

2001 ◽  
Vol 16 (36) ◽  
pp. 2353-2357 ◽  
Author(s):  
Y. S. MYUNG
Keyword(s):  
Black Hole ◽  
Central Charge ◽  
Three Dimensional ◽  
De Sitter Space ◽  
De Sitter ◽  
Correct Definition ◽  
Conical Defect ◽  
Entropy Bounds ◽  
Definition Of ◽  
Cardy Formula

We study the three-dimensional Schwarzschild–de Sitter ( SdS 3) black hole which corresponds essentially to a conical defect. We compute the mass of the SdS 3 black hole from the correct definition of the mass in asymptotically de Sitter space. Then we clarify the relation between the mass, entropy and temperature for this black hole without any ambiguity. We also establish the SdS 3/ CFT 2-correspondence for the entropy by applying the Cardy formula to a CFT with a central charge c = 3ℓ/2G3. Finally we discuss the entropy bounds for the SdS 3 black hole.

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