# Extending the ADM formalism to Weyl geometry

## Abstract

In order to treat quantum cosmology in the framework of Weyl spacetimes we take the first step of extending the Arnowitt-Deser-Misner formalism to Weyl geometry. We then obtain an expression of the curvature tensor in terms of spatial quantities by splitting spacetime in (3+l)-dimensional form. We next write the Lagrangian of the gravitation field based in Weyl-type gravity theory. We extend the general relativistic formalism in such a way that it can be applied to investigate the quantum cosmology of models whose spacetimes are endowed with a Weyl geometrical structure.

- Authors:

- Departamento de Física, Universidade Federal da Paraíba, João Pessoa, PB 58059-970 (Brazil)

- Publication Date:

- OSTI Identifier:
- 22391033

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1647; Journal Issue: 1; Conference: Conference on Cosmology and Gravitation in the Southern Cone, Valparaiso (Chile), 27-31 May 2013; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL MODELS; GEOMETRY; GRAVITATION; GRAVITATIONAL FIELDS; LAGRANGIAN FUNCTION; QUANTUM COSMOLOGY; RELATIVISTIC RANGE; SPACE-TIME; TENSORS

### Citation Formats

```
Barreto, A. B., Almeida, T. S., and Romero, C.
```*Extending the ADM formalism to Weyl geometry*. United States: N. p., 2015.
Web. doi:10.1063/1.4913344.

```
Barreto, A. B., Almeida, T. S., & Romero, C.
```*Extending the ADM formalism to Weyl geometry*. United States. doi:10.1063/1.4913344.

```
Barreto, A. B., Almeida, T. S., and Romero, C. Thu .
"Extending the ADM formalism to Weyl geometry". United States.
doi:10.1063/1.4913344.
```

```
@article{osti_22391033,
```

title = {Extending the ADM formalism to Weyl geometry},

author = {Barreto, A. B. and Almeida, T. S. and Romero, C.},

abstractNote = {In order to treat quantum cosmology in the framework of Weyl spacetimes we take the first step of extending the Arnowitt-Deser-Misner formalism to Weyl geometry. We then obtain an expression of the curvature tensor in terms of spatial quantities by splitting spacetime in (3+l)-dimensional form. We next write the Lagrangian of the gravitation field based in Weyl-type gravity theory. We extend the general relativistic formalism in such a way that it can be applied to investigate the quantum cosmology of models whose spacetimes are endowed with a Weyl geometrical structure.},

doi = {10.1063/1.4913344},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1647,

place = {United States},

year = {Thu Mar 26 00:00:00 EDT 2015},

month = {Thu Mar 26 00:00:00 EDT 2015}

}

DOI: 10.1063/1.4913344

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