Microcanonical functional integral for the gravitational field

Brown, J. David; York, James W.

doi:10.1103/physrevd.47.1420

Cited by 247 publications

(432 citation statements)

References 18 publications

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“…Such spacetimes are defined by the ambient metric defining conditions 1)-3) in section 2 of [13] (see also the conditions a)-d) in Problem 5.1 of this reference). 18 For the interpretation of β as a thermodynamic variable, see [35,36] and references therein.…”

Section: Ricci-flat Asymptoticsmentioning

confidence: 99%

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Costa

2012

J. High Energ. Phys.

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In this work we elaborate on an extension of the AdS/CFT framework to a subclass of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of conformal field theories on a codimension two manifold at null infinity. By truncating the gravity theory to the pure gravitational sector, we find the most general spacetime asymptotics, renormalize the gravitational action, reproduce the holographic stress tensors and Ward identities of the family of CFTs and show how the asymptotics is mapped to and reconstructed from conformal field theory data. In even dimensions, the holographic Weyl anomalies identify the bulk time coordinate with the spectrum of central charges with characteristic length the bulk Planck length. Consistency with locality in the bulk time direction requires a notion of locality in this spectrum.

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Section: Ricci-flat Asymptoticsmentioning

confidence: 99%

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Costa

2012

J. High Energ. Phys.

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“…The latter relations appear to hold in the present context (i.e., higher curvatures and/or higher dimensions), and it may be possible to prove them by extending the methods of Ref. [10]. One might expect that S coincides with one quarter the surface area of the horizon [11] as in Einstein gravity, but this identity fails in Lovelock gravity [7,8], and other higher curvature theories [12].…”

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confidence: 99%

Black hole entropy and higher curvature interactions

1993

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“…Notice also that we have implicitly worked with a microcanonical ensemble of universes, given our Boltzmannian interpretation of the holographic entropy. (Some aspects of the microcanonical ensemble for gravity have been discussed in [17]. )…”

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Probable Values of the Cosmological Constant in a Holographic Theory

2000

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We point out that for a large class of universes, holography implies that the most probable value for the cosmological constant is zero. In four space-time dimensions, the probability distribution takes the Baum-Hawking form, dP ϳ exp͑cM 2 p ͞L͒dL. The cosmological constant problem has a twofold meaning: It is a problem of fundamental physics, because the value of the cosmological constant L is tied to vacuum energy density. On the other hand, the cosmological constant tells us something about the large scale behavior of the universe, since a small cosmological constant implies that the observable universe is big and (nearly) flat. The problem is that there is an enormous discrepancy between the value of the vacuum energy density as predicted by quantum field theory of the standard-model degrees of freedom and the cosmologically observed value of L [2]. This discrepancy occurs already at very low-energy scales, of the order of eV, and clearly represents the most flagrant naturalness problem in today's physics.Thus, the cosmological constant relates the properties of the microscopic physics of the vacuum to the long-distance physics on cosmic scales. [This general philosophy was stressed in the wormhole approach to the cosmological constant problem (see [3] for the original references and [4,5] for a critique of this approach).] Therefore, the observable smallness of the cosmological constant should tell us something fundamental about the underlying microscopic theory of nature.In this note we study implications of holography [6,7], taken as a fundamental property of the microscopic theory of quantum gravity, for the cosmological constant problem. Assuming that the cosmological constant is a random variable, and that holographic entropy can be given a Boltzmannian interpretation, we point out that the most probable value of the cosmological constant in a holographic theory is zero, in ensembles of universes with finite-area holographic screens.It is not the aim of this paper to discuss the microscopic origin of any of these assumptions. In particular, the microscopic origin of holography and the randomness of the cosmological constant are clearly difficult problems whose solutions we do not claim to have understood. It is our goal to show that once these assumptions are satisfied, a simple and robust phenomenological argument implies a naturally small cosmological constant.

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Microcanonical functional integral for the gravitational field

Cited by 247 publications

References 18 publications

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Black hole entropy and higher curvature interactions

Probable Values of the Cosmological Constant in a Holographic Theory

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