Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem
arXiv:0808.1212 · doi:10.1088/0264-9381/26/4/045008
Abstract
We present a detailed analysis of the 3+1-split formalism of gravity in the presence of a cosmological constant. The formalism helps revealing the intimate connection between holography and the initial value formulation of gravity. We show that the various methods of holographic subtraction of divergences correspond just to different transformations of the canonical variables, such that the initial value problem is properly set up at the boundary. The renormalized boundary energy momentum tensor is a component of the Weyl tensor.
28 pages; v2: minor improvements, references added
References in corpus (36)
- The Dynamics of General Relativity
- A Stress Tensor for Anti-de Sitter Gravity
- Building an AdS/CFT superconductor
- Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
- Lecture Notes on Holographic Renormalization
- Gauge Symmetry and Supersymmetry of Multiple M2-Branes
- Algebraic structures on parallel M2-branes
- Modeling Multiple M2's
- Comments on Multiple M2-branes
- The gravity dual of a p-wave superconductor
- Quantum critical transport, duality, and M-theory
- Setting the boundary free in AdS/CFT
- Hall conductivity from dyonic black holes
- Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
- Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
- Ohm's Law at strong coupling: S duality and the cyclotron resonance
- Conserved charges for gravity with locally AdS asymptotics
- Quantum gravity with a positive cosmological constant
- Dynamics in Non-Globally-Hyperbolic Static Spacetimes II: General Analysis of Prescriptions for Dynamics
- Regularization of odd-dimensional AdS gravity: Kounterterms
- SL(2,Z) Action on Three-Dimensional CFTs and Holography
- Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems
- Nut Charged Space-times and Closed Timelike Curves on the Boundary
- Finite action principle for Chern-Simons AdS gravity
- SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
- Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4
- The Ambient Obstruction Tensor and Q-Curvature
- A holographic formulation of quantum general relativity
- Gravitational Duality Transformations on (A)dS4
- Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary
- Adding flavour to the Polchinski-Strassler background
- General Relativity from a gauged WZW term
- The Universe as a topological defect
- Electric-magnetic Duality and Deformations of Three-Dimensional CFT's
- Holographic Aspects of Electric-Magnetic Dualities
- Some considerations on the Mac Dowell-Mansouri action
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- Torsional degrees of freedom in AdS4/CFT3
- Electric/magnetic duality of dyonic Kerr-Newman-NUT-AdS spacetimes
- Radiation in Fluid/Gravity and the Flat Limit
- Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
- The Robinson-Trautman spacetime and its holographic fluid
- Gravitational duality, topologically massive gravity and holographic fluids
- Self-dual gravitational instantons and geometric flows of all Bianchi types