Focusing and the Holographic Hypothesis

Abstract

The ``screen mapping" introduced by Susskind to implement 't Hooft's holographic hypothesis is studied. For a single screen time, there are an infinite number of images of a black hole event horizon, almost all of which have smaller area on the screen than the horizon area. This is consistent with the focusing equation because of the existence of focal points. However, the {\it boundary} of the past (or future) of the screen obeys the area theorem, and so always gives an expanding map to the screen, as required by the holographic hypothesis. These considerations are illustrated with several axisymmetric static black hole spacetimes.

8 pages, plain latex, 5 figures included using psfig

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• TASI lectures on the Holographic Principle
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• Black holes are one-dimensional
• Chaotic motion in multi-black hole spacetimes and holographic screens
• Topological Holography
• On the Holographic RG-flow and the Low-energy, Strong Coupling, Large N Limit
• Quasi-local holography and quasi-local mass of classical fields in Minkowski spacetime
• RG Flow and Thermodynamics of Causal Horizons in Higher-Derivative AdS Gravity
• State reduction and energy extraction from black holes
• Comments on the entropic gravity proposal
• Entropic considerations on the Universe and Universe-Black Hole Systems
• Two Black Hole Holography, Lensing and Intensity
• Bousso's Covariant Entropy Bound and Padmanabhan's Emergent Universe