Quantum buoyancy, generalized second law, and higher-dimensional entropy bounds

Bekenstein has presented evidence for the existence of a universal upper bound of magnitude $2\pi R/\hbar c$ to the entropy-to-energy ratio $S/E$ of an arbitrary {\it three} dimensional system of proper radius $R$ and negligible self-gravity. In this paper we derive a generalized upper bound on the entropy-to-energy ratio of a $(D+1)$-dimensional system. We consider a box full of entropy lowered towards and then dropped into a $(D+1)$-dimensional black hole in equilibrium with thermal radiation. In the canonical case of three spatial dimensions, it was previously established that due to quantum buoyancy effects the box floats at some neutral point very close to the horizon. We find here that the significance of quantum buoyancy increases dramatically with the number $D$ of spatial dimensions. In particular, we find that the neutral (floating) point of the box lies near the horizon only if its length $b$ is large enough such that $b/b_C>F(D)$, where $b_C$ is the Compton length of the body and $F(D)\sim D^{D/2}\gg1$ for $D\gg1$. A consequence is that quantum buoyancy severely restricts our ability to deduce the universal entropy bound from the generalized second law of thermodynamics in higher-dimensional spacetimes with $D\gg1$. Nevertheless, we find that the universal entropy bound is always a sufficient condition for operation of the generalized second law in this type of gedanken experiments.Comment: 6 page

Probing Quantum Geometry at LHC

We present an evidence, that the volumes of compactified spaces as well as the areas of black hole horizons must be quantized in Planck units. This quantization has phenomenological consequences, most dramatic being for micro black holes in the theories with TeV scale gravity that can be produced at LHC. We predict that black holes come in form of a discrete tower with well defined spacing. Instead of thermal evaporation, they decay through the sequence of spontaneous particle emissions, with each transition reducing the horizon area by strictly integer number of Planck units. Quantization of the horizons can be a crucial missing link by which the notion of the minimal length in gravity eliminates physical singularities. In case when the remnants of the black holes with the minimal possible area and mass of order few TeV are stable, they might be good candidates for the cold dark matter in the Universe.Comment: 14 pages, Late

On the Origin of Gravity and the Laws of Newton

Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.Comment: 29 pages, 6 figure

Effective temperature for black holes

The physical interpretation of black hole's quasinormal modes is fundamental for realizing unitary quantum gravity theory as black holes are considered theoretical laboratories for testing models of such an ultimate theory and their quasinormal modes are natural candidates for an interpretation in terms of quantum levels. The spectrum of black hole's quasinormal modes can be re-analysed by introducing a black hole's effective temperature which takes into account the fact that, as shown by Parikh and Wilczek, the radiation spectrum cannot be strictly thermal. This issue changes in a fundamental way the physical understanding of such a spectrum and enables a re-examination of various results in the literature which realizes important modifies on quantum physics of black holes. In particular, the formula of the horizon's area quantization and the number of quanta of area result modified becoming functions of the quantum "overtone" number n. Consequently, the famous formula of Bekenstein-Hawking entropy, its sub-leading corrections and the number of microstates are also modified. Black hole's entropy results a function of the quantum overtone number too. We emphasize that this is the first time that black hole's entropy is directly connected with a quantum number. Previous results in the literature are re-obtained in the limit n \to \infty.Comment: 10 pages,accepted for publication in Journal of High Energy Physics. Comments are welcom

Black holes and information theory

During the past three decades investigators have unveiled a number of deep connections between physical information and black holes whose consequences for ordinary systems go beyond what has been deduced purely from the axioms of information theory. After a self-contained introduction to black hole thermodynamics, we review from its vantage point topics such as the information conundrum that emerges from the ability of incipient black holes to radiate, the various entropy bounds for non-black hole systems (holographic bound, universal entropy bound, etc) which are most easily derived from black hole thermodynamics, Bousso's covariant entropy bound, the holographic principle of particle physics, and the subject of channel capacity of quantum communication channels.Comment: RevTeX, 12 pages, 5 figures. To appear in Contemporary Physic

The holographic principle

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.Comment: 52 pages, 10 figures, invited review for Rev. Mod. Phys; v2: reference adde

The ideal energy of classical lattice dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335

The entropy of black holes: a primer

After recalling the definition of black holes, and reviewing their energetics and their classical thermodynamics, one expounds the conjecture of Bekenstein, attributing an entropy to black holes, and the calculation by Hawking of the semi-classical radiation spectrum of a black hole, involving a thermal (Planckian) factor. One then discusses the attempts to interpret the black-hole entropy as the logarithm of the number of quantum micro-states of a macroscopic black hole, with particular emphasis on results obtained within string theory. After mentioning the (technically cleaner, but conceptually more intricate) case of supersymmetric (BPS) black holes and the corresponding counting of the degeneracy of Dirichlet-brane systems, one discusses in some detail the ``correspondence'' between massive string states and non-supersymmetric Schwarzschild black holes.Comment: 51 pages, 4 figures, talk given at the "Poincare seminar" (Paris, 6 December 2003), to appear in Poincare Seminar 2003 (Birkhauser

Large entropy production inside black holes: a simple model

Particles dropped into a rotating black hole can collide near the inner horizon with enormous energies. The entropy produced by these collisions can be several times larger than the increase in the horizon entropy due to the addition of the particles. In this paper entropy is produced by releasing large numbers of neutrons near the outer horizon of a rotating black hole such that they collide near the inner horizon at energies similar to those achieved at the Relativistic Heavy Ion Collider. The increase in horizon entropy is approximately 80 per dropped neutron pair, while the entropy produced in the collisions is 160 per neutron pair. The collision entropy is produced inside the horizon, so this excess entropy production does not violate Bousso's bound limiting the entropy that can go through the black hole's horizon. The generalized laws of black hole thermodynamics are obeyed. No individual observer inside the black hole sees a violation of the second law of thermodynamicsComment: 10 page

Black hole microstate geometries from string amplitudes

In this talk we review recent calculations of the asymptotic supergravity fields sourced by bound states of D1 and D5-branes carrying travelling waves. We compute disk one-point functions for the massless closed string fields. At large distances from the branes, the effective open string coupling is small, even in the regime of parameters where the classical D1-D5-P black hole may be considered. The fields sourced by the branes differ from the black hole solution by various multipole moments, and have led to the construction of a new 1/8-BPS ansatz in type IIB supergravity.Comment: 14 pages, 3 figures, Contribution to the proceedings of the Black Objects in Supergravity School, Frascati, 201