The Holographic Principle for General Backgrounds

We aim to establish the holographic principle as a universal law, rather than a property only of static systems and special space-times. Our covariant formalism yields an upper bound on entropy which applies to both open and closed surfaces, independently of shape or location. It reduces to the Bekenstein bound whenever the latter is expected to hold, but complements it with novel bounds when gravity dominates. In particular, it remains valid in closed FRW cosmologies and in the interior of black holes. We give an explicit construction for obtaining holographic screens in arbitrary space-times (which need not have a boundary). This may aid the search for non-perturbative definitions of quantum gravity in space-times other than AdS.Comment: 15 pages, 4 figures. Based on a talk given at Strings '99. Includes a reply to recent criticism. For more details, examples, and references, see hep-th/9905177 and hep-th/990602

The nonlinear evolution of de Sitter space instabilities

We investigate the quantum evolution of large black holes that nucleate spontaneously in de Sitter space. By numerical computation in the s-wave and one-loop approximations, we verify claims that such black holes can initially "anti-evaporate" instead of shrink. We show, however, that this is a transitory effect. It is followed by an evaporating phase, which we are able to trace until the black holes are small enough to be treated as Schwarzschild. Under generic perturbations, the nucleated geometry is shown to decay into a ring of de Sitter regions connected by evaporating black holes. This confirms that de Sitter space is globally unstable and fragments into disconnected daughter universes.Comment: 10 pages, 8 figures, to appear in PR

Unified approach to study quantum properties of primordial black holes, wormholes and of quantum cosmology

We review the anomaly induced effective action for dilaton coupled spinors and scalars in large N and s-wave approximation. It may be applied to study the following fundamental problems: construction of quantum corrected black holes (BHs), inducing of primordial wormholes in the early Universe (this effect is confirmed) and the solution of initial singularity problem. The recently discovered anti-evaporation of multiple horizon BHs is discussed. The existance of such primordial BHs may be interpreted as SUSY manifestation. Quantum corrections to BHs thermodynamics maybe also discussed within such scheme.Comment: LaTeX file and two eps files, to appear in MPLA, Brief Review

Quantum Global Structure of de Sitter Space

I study the global structure of de Sitter space in the semi-classical and one-loop approximations to quantum gravity. The creation and evaporation of neutral black holes causes the fragmentation of de Sitter space into disconnected daughter universes. If the black holes are stabilized by a charge, I find that the decay leads to a necklace of de Sitter universes (`beads') joined by near-extremal black hole throats. For sufficient charge, more and more beads keep forming on the necklace, so that an unbounded number of universes will be produced. In any case, future infinity will not be connected. This may have implications for a holographic description of quantum gravity in de Sitter space.Comment: 37 pages, LaTeX2e, 10 figures. v2: references adde

Probing entropy bounds with scalar field spacetimes

We study covariant entropy bounds in dynamical spacetimes with naked singularities. Specifically we study a spherically symmetric massless scalar field solution. The solution is an inhomogeneous cosmology with an initial spacelike singularity, and a naked timelike singularity at the origin. We construct the entropy flux 4-vector for the scalar field, and show by explicit computation that the generalized covariant bound $S_{L(B,B')}\le (A(B)-A(B'))/4$ is violated for light sheets $L(B,B')$ in the neighbourhood of the (evolving) apparent horizon. We find no violations of the Bousso bound (for which $A(B')=0$), even though certain sufficient conditions for this bound do not hold. This result therefore shows that these conditions are not necessary.Comment: 10 pages, 5 figures; published version with typos correcte

Can Quantum-Corrected BTZ Black Hole Anti-Evaporate?

Kaluza-Klein reduction of 3D gravity with minimal scalars leads to 2D dilaton-Maxwell gravity with dilaton coupled scalars. Evaluating the one-loop effective action for dilaton coupled scalars in large $N$ and s-wave approximation we apply it to study quantum evolution of BTZ black hole. It is shown that quantum-corrected BTZ BH may evaporate or else anti-evaporate similarly to 4D Nariai BH as is observed by Bousso and Hawking. Instable higher modes in the spectrum indicate also the possibility of proliferation of BTZ BH.Comment: LaTeX file and ps file of figure

Thermodynamics of Schwarzschild-(Anti-)de Sitter Black Holes with account of quantum corrections

We discuss the quantum corrections to thermodynamics (and geometry) of S(A)dS BHs using large $N$ one-loop anomaly induced effective action for dilaton coupled matter (scalars and spinors). It is found the temperature, mass and entropy with account of quantum effects for multiply horizon SdS BH and SAdS BH what also gives the corresponding expressions for their limits: Schwarzschild and de Sitter spaces. In the last case one can talk about quantum correction to entropy of expanding Universe. The anomaly induced action under discussion corresponds to 4d formulation (s-wave approximation, 4d quantum matter is minimal one) as well as 2d formulation (complete effective action, 2d quantum matter is dilaton coupled one). Hence, most of results are given for the same gravitational background with interpretation as 4d quantum corrected BH or 2d quantum corrected dilatonic BH. Quantum aspects of thermodynamics of 4d 't Hooft BH model are also considered.Comment: LaTeX file, 28 pages, some misprints are correcte

Inflation as a response to protect the Holographic Principle

A model where the inflationary phase emerges as a response to protect the Fischler-Susskind holographic bound is described. A two fluid model in a closed universe inflation picture is assumed, and a discussion on conditions under which is possible to obtain an additional exponential expansion phase as those currently observed is given.Comment: 6 pages, 2 figures. Accepted for publication in MPL

Proliferation of de Sitter Space

I show that de Sitter space disintegrates into an infinite number of copies of itself. This occurs iteratively through a quantum process involving two types of topology change. First a handle is created semiclassically, on which multiple black hole horizons form. Then the black holes evaporate and disappear, splitting the spatial hypersurfaces into large parts. Applied to cosmology, this process leads to the production of a large or infinite number of universes in most models of inflation and yields a new picture of global structure.Comment: 19 pages, LaTeX2e, 4 figure

Holographic Domains of Anti-de Sitter Space

An AdS_4 brane embedded in AdS_5 exhibits the novel feature that a four-dimensional graviton is localized near the brane, but the majority of the infinite bulk away from the brane where the warp factor diverges does not see four-dimensional gravity. A naive application of the holographic principle from the point of view of the four-dimensional observer would lead to a paradox; a global holographic mapping would require infinite entropy density. In this paper, we show that this paradox is resolved by the proper covariant formulation of the holographic principle. This is the first explicit example of a time-independent metric for which the spacelike formulation of the holographic principle is manifestly inadequate. Further confirmation of the correctness of this approach is that light-rays leaving the brane intersect at the location where we expect four-dimensional gravity to no longer dominate. We also present a simple method of locating CFT excitations dual to a particle in the bulk. We find that the holographic image on the brane moves off to infinity precisely when the particle exits the brane's holographic domain. Our analysis yields an improved understanding of the physics of the AdS_4/AdS_5 model.Comment: 29 pages, 6 figure