Null infinity and extremal horizons in AdS-CFT

Abstract

We consider AdS gravity duals to CFT on background spacetimes with a null infinity. Null infinity on the conformal boundary may extend to an extremal horizon in the bulk. For example it does so for Poincare-AdS, although does not for planar Schwarzschild-AdS. If null infinity does extend into an extremal horizon in the bulk, we show that the bulk near-horizon geometry is determined by the geometry of the boundary null infinity. Hence the `infra-red' geometry of the bulk is fixed by the large scale behaviour of the CFT spacetime. In addition the boundary stress tensor must have a particular decay at null infinity. As an application, we argue that for CFT on asymptotically flat backgrounds, any static bulk dual containing an extremal horizon extending from the boundary null infinity, must have the near-horizon geometry of Poincare-AdS. We also discuss a class of boundary null infinity that cannot extend to a bulk extremal horizon, although we give evidence that they can extend to an analogous null surface in the bulk which possesses an associated scale-invariant `near-geometry'.

arXiv comment35 pages

References in corpus (17)

• An Alternative to Compactification
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• The AdS/CFT Correspondence and a New Positive Energy Conjecture for General Relativity
• Near-horizon symmetries of extremal black holes
• Asymptotically Anti-de Sitter spacetimes and their stress energy tensor
• Classification of near-horizon geometries of extremal black holes
• Gravity and large black holes in Randall-Sundrum II braneworlds
• Extremal vacuum black holes in higher dimensions
• On non-existence of static vacuum black holes with degenerate components of the event horizon
• Vortices in holographic superfluids and superconductors as conformal defects
• Unique continuation results for Ricci curvature and applications
• Black Funnels
• Black Droplets
• CFTs in rotating black hole backgrounds
• Rotating Black Droplet
• Two remarks on near-horizon geometries
• Charged Randall-Sundrum black holes and N=4 super Yang-Mills in AdS(2)xS(2)

Cited by in corpus (1)

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