Entropy Bounds: New Insights (original) (raw)

New holographic entropy bound from quantum geometry

Physical Review D, 2001

A new entropy bound, tighter than the standard holographic bound due to Bekenstein, is derived for spacetimes with non-rotating isolated horizons, from the quantum geometry approach in which the horizon is described by the boundary degrees of freedom of a three dimensional Chern Simons theory. *

Evidence for an entropy bound from fundamentally discrete gravity

Classical and Quantum Gravity, 2006

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, but should manifest itself in a theory of quantum gravity. We present a measure for the maximal entropy of spherically symmetric spacelike regions within the causal set approach to quantum gravity. In terms of the proposal, a bound for the entropy contained in this region can be derived from a counting of potential "degrees of freedom" associated to the Cauchy horizon of its future domain of dependence. For different spherically symmetric spacelike regions in Minkowski spacetime of arbitrary dimension, we show that this proposal leads, in the continuum approximation, to Susskind's well-known spherical entropy bound.

On geometric entropy

Physics Letters B, 1994

We show that a geometrical notion of entropy, definable in flat space, governs the first quantum correction to the Bekenstein-Hawking black hole entropy.

HOLOGRAPHIC GEOMETRIC ENTROPY AT FINITE TEMPERATURE FROM BLACK HOLES IN GLOBAL ANTI-DE SITTER SPACES

International Journal of Modern Physics A, 2012

Using a holographic proposal for the geometric entropy we study its behavior in the geometry of Schwarzschild black holes in global AdS p for p = 3, 4, 5. Holographically, the entropy is determined by a minimal surface. On the gravity side, due to the presence of a horizon on the background, generically there are two solutions to the surfaces determining the entanglement entropy. In the case of AdS 3 , the calculation reproduces precisely the geometric entropy of an interval of length l in a two dimensional conformal field theory with periodic boundary conditions. We demonstrate that in the cases of AdS 4 and AdS 5 the sign of the difference of the geometric entropies changes, signaling a transition. Euclideanization implies that various embedding of the holographic surface are possible. We study some of them and find that the transitions are ubiquitous. In particular, our analysis renders a very intricate phase space, showing, for some ranges of the temperature, up to three branches. We observe a remarkable universality in the type of results we obtain from AdS 4 and AdS 5 .

On the behavior of the bounds of the holographic theory for massive and massless particle systems

The aim of the present dissertation is to analyze the meaning of the entropy bounds of the holographic sector once tested for statistical ensembles of particles, in order to deeper investigate the nature of these constraints and their mutual links. From the Universal Ener- gy Bound (UEB) simple time constraints can be argued, which are manifestations of the discrete nature of the space-time and of the presence of ultimate space-time scales. From the combined effort of the UEB and of the Holographic bound by `t Hooft and Susskind, an entropy density bound as a function of temperature is achieved.

Black Hole Entropy: Certain Quantum Features

On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (In 3 Volumes), 2002

The issue of black hole entropy is reexamined within a finite lattice framework along the lines of Wheeler, 't Hooft and Susskind, with an additional criterion to identify physical horizon states contributing to the entropy. As a consequence, the degeneracy of physical states is lower than that attributed normally to black holes. This results in corrections to the Bekenstein-Hawking area law that are logarithmic in the horizon area. Implications for the holographic entropy bound on bounded spaces are discussed. Theoretical underpinnings of the criterion imposed on the states, based on the 'quantum geometry' formulation of quantum gravity, are briefly explained.

Holographic holes and differential entropy

Journal of High Energy Physics, 2014

Recently it has been shown that the Bekenstein-Hawking entropy formula evaluated on certain closed surfaces in the bulk of a holographic spacetime has an interpretation as the differential entropy of a particular family of intervals (or strips) in the boundary theory [1, 2]. We first extend this construction to bulk surfaces which vary in time. We then give a general proof of the equality between the gravitational entropy and the differential entropy. This proof applies to a broad class of holographic backgrounds possessing a generalized planar symmetry and to certain classes of higher-curvature theories of gravity. To apply this theorem, one can begin with a bulk surface and determine the appropriate family of boundary intervals by considering extremal surfaces tangent to the given surface in the bulk. Alternatively, one can begin with a family of boundary intervals; as we show, the differential entropy then equals the gravitational entropy of a bulk surface that emerges from the intersection of the neighboring entanglement wedges, in a continuum limit.

Holography, degenerate horizons and entropy

Nuclear Physics B, 2000

We show that a realization of the correspondence AdS 2 /CFT 1 for near extremal Reissner-Nordström black holes in arbitrary dimensional Einstein-Maxwell gravity exactly reproduces, via Cardy's formula, the deviation of the Bekenstein-Hawking entropy from extremality. We also show that this mechanism is valid for Schwarzschild-de Sitter black holes around the degenerate solution dS 2 ×S n. These results reinforce the idea that the Bekenstein-Hawking entropy can be derived from symmetry principles.

Relative entropy and holography

Journal of High Energy Physics, 2013

Relative entropy between two states in the same Hilbert space is a fundamental statistical measure of the distance between these states. Relative entropy is always positive and increasing with the system size. Interestingly, for two states which are infinitesimally different to each other, vanishing of relative entropy gives a powerful 2 This inequality can be regarded as a generalized statement of the Bekenstein bound which holds for any region in QFT. This is explained in more detail in the appendix A.4.

Geometric Framework for Entropy in General Relativity

We introduce a covariant and geometrical framework for entropy in relativistic theories. In this framework the entropy of gravitational systems turns out to be a geometric quantity with well-defined cohomological properties arising from the obstruction to foliating spacetime into spacelike hypersurfaces. The framework relies on general covariance within a geometric framework which was recently defined to deal with the variation of conserved quantities generated by Nöther theorem. The definition of gravitational entropy so obtained turns out to be very general: it can be generalized to causal horizons and multiple-horizon spacetimes and it can be applied to define entropy for more exotic singular solutions of Einstein field equations. The same definition is also well-suited for higher dimensions and in the case of alternative gravitational theories (e.g. Chern-Simons theories and Lovelock Gravity).