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.