Related papers: Outer entropy = Bartnik-Bray inner mass, and the g…
Behind certain marginally trapped surfaces one can construct a geometry containing an extremal surface of equal, but not larger area. This construction underlies the Engelhardt-Wall proposal for explaining Bekenstein-Hawking entropy as a…
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…
Given a sphere with Bartnik data close to that of a round sphere in Euclidean 3-space, we compute its Bartnik-Bray outer mass to first order in the data's deviation from the standard sphere. The Hawking mass gives a well-known lower bound,…
In any static spacetime the quasilocal Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics, and…
We examine the idea that in quantum gravity, the entanglement entropy of a general region should be finite and the leading contribution is given by the Bekenstein-Hawking area law. Using holographic entanglement entropy calculations, we…
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…
In this paper we characterize the intrinsic geometry of apparent horizons (outermost marginally outer trapped surfaces) in asymptotically flat spacetimes; that is, the Riemannian metrics on the two sphere which can arise. Furthermore we…
Gravity is a macroscopic manifestation of a microscopic quantum theory of space-time, just as the theories of elasticity and hydrodynamics are the macroscopic manifestation of the underlying quantum theory of atoms. The connection of…
Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to…
The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…
On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation.…
Theories of emergent gravity have established a deep connection between entropy and the geometry of spacetime by looking at the latter through a thermodynamic lens. In this framework, the macroscopic properties of gravity arise in a…
The definition of quasi-local mass for a bounded space-like region in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary…
Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which…
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in…
Entropy of all systems that we understand well is proportional to their volumes except for black holes given by their horizon area. This makes the microstates of any quantum theory of gravity drastically different from the ordinary matter.…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
We introduce R\'enyi entropy of a subsystem energy as a natural quantity which closely mimics the behavior of the entanglement entropy and can be defined for all the quantum many body systems. For this purpose, consider a quantum chain in…
For a large class of density matrices in semiclassical gravity, it is shown that the reduced density matrix which corresponds to tracing over the degrees of freedom in a spatial subregion is dominated by states for which the area of the…
A dynamical estimate is given for the Boltzmann entropy of the Universe, under the simplifying assumptions provided by Newtonian cosmology. We first model the cosmological fluid as the probability fluid of a quantum-mechanical system. Next,…