skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum geometry and gravitational entropy

Abstract

Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
Physics Division
OSTI Identifier:
934489
Report Number(s):
LBNL-412E
TRN: US0803916
DOE Contract Number:
DE-AC02-05CH11231
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of High Energy Physics; Journal Volume: 2007; Journal Issue: 12; Related Information: Journal Publication Date: 18 December 2007
Country of Publication:
United States
Language:
English
Subject:
72; EIGENSTATES; ENTROPY; GEOMETRY; HILBERT SPACE; METRICS; SPACE-TIME; TOPOLOGY; AdS-CFT Correspondence; Black Holes in String Theory; Gauge-gravity correspondence

Citation Formats

Simon, Joan, Balasubramanian, Vijay, Czech, Bart Iomiej, Larjo, Klaus, Marolf, Donald, and Simon, Joan. Quantum geometry and gravitational entropy. United States: N. p., 2007. Web.
Simon, Joan, Balasubramanian, Vijay, Czech, Bart Iomiej, Larjo, Klaus, Marolf, Donald, & Simon, Joan. Quantum geometry and gravitational entropy. United States.
Simon, Joan, Balasubramanian, Vijay, Czech, Bart Iomiej, Larjo, Klaus, Marolf, Donald, and Simon, Joan. Tue . "Quantum geometry and gravitational entropy". United States. doi:. https://www.osti.gov/servlets/purl/934489.
@article{osti_934489,
title = {Quantum geometry and gravitational entropy},
author = {Simon, Joan and Balasubramanian, Vijay and Czech, Bart Iomiej and Larjo, Klaus and Marolf, Donald and Simon, Joan},
abstractNote = {Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.},
doi = {},
journal = {Journal of High Energy Physics},
number = 12,
volume = 2007,
place = {United States},
year = {Tue May 29 00:00:00 EDT 2007},
month = {Tue May 29 00:00:00 EDT 2007}
}
  • The precise analog of the {theta}-quantization ambiguity of Yang-Mills theory exists for the real SU(2) connection formulation of general relativity. As in the former case {theta} labels representations of large gauge transformations, which are superselection sectors in loop quantum gravity. We show that unless {theta}=0, the (kinematical) geometric operators such as area and volume are not well defined on spin network states. More precisely the intersection of their domain with the dense set Cyl in the kinematical Hilbert space H of loop quantum gravity is empty. The absence of a well-defined notion of area operator acting on spin network statesmore » seems at first in conflict with the expected finite black hole entropy. However, we show that the black hole (isolated) horizon area--which in contrast to kinematical area is a (Dirac) physical observable--is indeed well defined, and quantized so that the black hole entropy is proportional to the area. The effect of {theta} is negligible in the semiclassical limit where proportionality to area holds.« less
  • Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the 'quantum potential' that leads to the Schr√∂dinger equation follows naturally from information geometry.
  • We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iteratingmore » a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.« less
  • This paper reexamines the statistical quantum field theory of a free, minimally coupled, real scalar field Phi in a statically bounded, classical Friedmann cosmology, where the time-dependent scale factor ..cap omega..(t) tends to constant values ..cap omega../sub 1/ and ..cap omega../sub 2/ for tt/sub 2/. The principal objective is to investigate the intuition that ''entropy'' S correlates with average particle number , so that increases in induced by parametric amplification manifest a one-to-one connection with increases in S. The definition of particle number N/sub k/ becomes unambiguous for t>t/sub 2/ and t
  • There is a conjecture due to Penrose that there may be a relation between the Weyl curvature tensor and gravitational entropy. In this paper, this conjecture is studied in the context of a specific model, the Gowdy cosmology. The square of the curvature is calculated as an operator and its expectation values in states of clumped and unclumped gravitons are calculated. The results indicate that the curvature contains information about the entropy of the gravitational field.