Outer Entropy and Quasilocal Energy

Abstract

We define the coarse-grained entropy of a `normal' surface $\sigma$, i.e., a surface that is neither trapped nor antitrapped. Following Engelhardt and Wall, the entropy is defined in terms of the area of an auxiliary extremal surface. This area is maximized over all auxiliary geometries that can be constructed in the interior of $\sigma$, while holding fixed the spatial exterior (the outer wedge). We argue that the area is maximized when the stress tensor in the auxiliary geometry vanishes, and we develop a formalism for computing it under this assumption. The coarse-grained entropy can be interpreted as a quasilocal energy of $\sigma$. This energy possesses desirable properties such as positivity and monotonicity, which derive directly from its information-theoretic definition.

40 pages, 3 figures

References in corpus (9)

• Relative entropy and the Bekenstein bound
• Deriving covariant holographic entanglement
• Proof of a Quantum Bousso Bound
• Entropy on a null surface for interacting quantum field theories and the Bousso bound
• The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions
• Angular momentum conservation for dynamical black holes
• The Boundary of the Future
• Deformation of Codimension-2 Surface and Horizon Thermodynamics
• Dynamics and Observer-Dependence of Holographic Screens

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• Local gravitational energy in higher dimensions