# 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}

}