Outer entropy and quasilocal energy

Abstract

We define the coarse-grained entropy of a "normal" surface σ, 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 σ, 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 σ. This energy possesses desirable properties such as positivity and monotonicity, which derive directly from its information-theoretic definition.

The small sphere limit of quasilocal energy in higher dimensions along lightcone cuts

“…Remark 4.2. The same generalisation of the Hawking energy M 0 has been studied in [5] and appears in a discussion of quasilocal energy in [17]. The original definition by Hayward [9] also contains an anholonomicity term, but it is gauge dependent (See discussions in sections 6.3 and 4.1.8 in [7]).…”

Holographic argument for the Penrose inequality in AdS spacetimes

“…al. [30] proposed that the outer entropy of a normal surface ν should be thought of as defining a quasi-local mass M ν associated to ν. They defined M ν using the relation between mass and area of a Schwarzschild black hole.…”

“…However, since we are considering asymptotically AdS spacetimes, it seems more appropriate to use the Schwarzschild AdS solution. In four dimensions, this AdS version of the proposal in [30] is…”

“…al. [30] also construct a generalization of the doubled spacetime construction reviewed in Sec. 2 for normal surfaces.…”

“…There are applications of the AdS Penrose inequality to the area law for apparent horizons [25][26][27][28][29] and a proposed quasilocal mass formula [30]. We will discuss these applications in Sec.…”