scholarly journals Asymptotic Properties of Linear Field Equations in Anti-de Sitter Space

2019 ◽  
Vol 374 (2) ◽  
pp. 1125-1178 ◽  
Author(s):  
Gustav Holzegel ◽  
Jonathan Luk ◽  
Jacques Smulevici ◽  
Claude Warnick
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Properties ◽  
Uniform Boundedness ◽  
Global Dynamics ◽  
Decay Estimates ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Spacetime ◽  
Loss Of Derivatives ◽  
Dissipative Boundary

Abstract We study the global dynamics of the wave equation, Maxwell’s equation and the linearized Bianchi equations on a fixed anti-de Sitter (AdS) background. Provided dissipative boundary conditions are imposed on the dynamical fields we prove uniform boundedness of the natural energy as well as both degenerate (near the AdS boundary) and non-degenerate integrated decay estimates. Remarkably, the non-degenerate estimates “lose a derivative”. We relate this loss to a trapping phenomenon near the AdS boundary, which itself originates from the properties of (approximately) gliding rays near the boundary. Using the Gaussian beam approximation we prove that non-degenerate energy decay without loss of derivatives does not hold. As a consequence of the non-degenerate integrated decay estimates, we also obtain pointwise-in-time decay estimates for the energy. Our paper provides the key estimates for a proof of the non-linear stability of the anti-de Sitter spacetime under dissipative boundary conditions. Finally, we contrast our results with the case of reflecting boundary conditions.

scholarly journals Designer de Sitter spacetimes

2008 ◽  
Vol 86 (4) ◽  
pp. 591-595
Author(s):  
K Schleich ◽  
D M Witt
Keyword(s):  
Cosmological Constant ◽  
Infinite Family ◽  
Einstein Equations ◽  
Global Dynamics ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Isotropic Solution ◽  
Accelerating Expansion ◽  
Sitter Spacetime ◽  
Expansion Of The Universe

Recent observations in cosmology indicate an accelerating expansion of the Universe postulated to arise from some form of dark energy, the paradigm being positive cosmological constant. De Sitter spacetime is the well-known isotropic solution to the Einstein equations with cosmological constant. However, as discussed here, it is not the most general, locally isotropic solution. One can construct an infinite family of such solutions, designer de Sitter spacetimes, which are everywhere locally isometric to a region of de Sitter spacetime. However, the global dynamics of these designer cosmologies is very different than that of de Sitter spacetime itself. The construction and dynamics of these designer de Sitter spacetimes is detailed along with some comments about their implications for the structure of our Universe.PACS Nos.: 04.20.–q, 04.20.Ex, 04.20.Gz, 98.80.–k

scholarly journals TORSION CORRECTIONS IN BRANE WORLD GRAVITY

2011 ◽  
Vol 03 ◽  
pp. 150-160 ◽  
Author(s):  
R. MAIER
Keyword(s):  
Cosmological Model ◽  
Extrinsic Curvature ◽  
Matter Content ◽  
Brane World ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Sitter Spacetime ◽  
World Theory

In the frame of brane world theory the effects of torsion fields are examined. Considering a five dimensional Non-Riemannian bulk with a noncompact extra dimension, we derive the modified Einstein field equations in a four dimensional (3-brane) arbitrary manifold embedded in this bulk. The necessary matching conditions are investigated assuming that the torsion in the bulk is continuous. In this context the extrinsic curvature is connected to the matter content restricted to the brane and the torsion components of the bulk. As a final result we observe that the corrections – due to torsion fields – in the modified field equations depend crucially on the embedding that is taken. Therefore, by considering a simple embedding, we develop a cosmological model that describes a flat FLRW embedded in a 5-dimensional de Sitter (or Anti de Sitter) spacetime, where a 5-dimensional cosmological constant emerges from the torsion components of the bulk.

scholarly journals The Einstein–Klein–Gordon–AdS system for general boundary conditions

2015 ◽  
Vol 12 (02) ◽  
pp. 293-342 ◽  
Author(s):  
Gustav Holzegel ◽  
Claude M. Warnick
Keyword(s):  
Boundary Conditions ◽  
Global Dynamics ◽  
Linear Wave ◽  
Spherically Symmetric ◽  
General Boundary Conditions ◽  
De Sitter ◽  
Linear Wave Equation ◽  
Starting Point ◽  
Klein Gordon ◽  
Local Solutions

We construct unique local solutions for the spherically-symmetric Einstein–Klein–Gordon–anti-de Sitter (AdS) system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence. The proof relies on estimates developed for the linear wave equation by the second author and involves a careful renormalization of the dynamical variables, including a renormalization of the well-known Hawking mass. For some of the boundary conditions considered this system is expected to exhibit rich global dynamics, including the existence of hairy black holes. This paper furnishes a starting point for such global investigations.

scholarly journals Unimodular vs nilpotent superfield approach to pure dS supergravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sukruti Bansal ◽  
Silvia Nagy ◽  
Antonio Padilla ◽  
Ivonne Zavala
Keyword(s):  
String Theory ◽  
General Framework ◽  
Recent Progress ◽  
High Energy ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
New Approach ◽  
Sitter Spacetime ◽  
Novel Approach ◽  
De Sitter Vacua

Abstract Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stückelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.

scholarly journals Wavefunctions in dS/CFT revisited: principal series and double-trace deformations

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hiroshi Isono ◽  
Hoiki Madison Liu ◽  
Toshifumi Noumi
Keyword(s):  
Principal Series ◽  
Light Fields ◽  
Quadratic Term ◽  
De Sitter Spacetime ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Complementary Series ◽  
Point Function ◽  
Sitter Spacetime ◽  
Simple Scaling

Abstract We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological horizon. As a consequence, the quadratic term in the wavefunction does not follow a simple scaling and so it is hard to identify it with a conformal two-point function. In this paper, we demonstrate that it should be interpreted as a two-point function on a cyclic RG flow which is obtained by double-trace deformations of the dual CFT. This is analogous to the situation in nonrelativistic AdS/CFT with a bulk scalar whose mass squared is below the Breitenlohner-Freedman (BF) bound. We also provide a new dS/CFT dictionary relating de Sitter two-point functions and conformal two-point functions in the would-be dual CFT.

Sign in / Sign up

Export Citation Format

Share Document