On the Holographic Nature Of Rindler Energy

Abstract

We show that the dimensionless Rindler energy of a black hole, $E_R$, is exactly the surface Hamiltonian obtained from the Einstein--Hilbert action evaluated on the horizon. Therefore, $E_R$ is given by a surface integral over the horizon and manifestly holographic. In the context of the AdS/CFT duality, Rindler energy corresponds, on the boundary, to a dimensionless energy given by the product of the AdS radius and the extensive part of the CFT energy. We find that, beyond General Relativity, $E_R$ is still holographic but not necessarily given by the surface Hamiltonian of the theory.

arXiv comment19 pages

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Cited by in corpus (8)

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• Liouville Theory on Horizons: Towards a Quantum Theory of Black Holes
• Extremal Black Hole Entropy from Horizon Conformal Field Theories
• The Holographic Entanglement Entropy of Schwarzschild Black Holes
• Complexity Near Horizons
• Schwarzschild Black Holes and Asymptotic $Ad{S}_2$
• Black Hole Entropy and the Pseudo Goldstone Bosons of Conformal Symmetry