# Geometrical aspects on the dark matter problem

## Abstract

In the present paper we apply Nash’s theory of perturbative geometry to the study of dark matter gravity in a higher-dimensional space–time. It is shown that the dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature of the standard cosmology. In order to test our model, we use a spherically symmetric metric embedded in a five-dimensional bulk. As a result, considering a sample of 10 low surface brightness and 6 high surface brightness galaxies, we find a very good agreement with the observed rotation curves of smooth hybrid alpha-HI measurements. - Highlights: • The metric perturbation and the embedding lead naturally to a “brane-world”-like higher dimensional structure. • Nash’s theorem as a cornerstone of the formation of geometrical structures. • The dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature. • A good agreement was found with the observed rotation curves of smooth hybrid alpha-HI measurements.

- Authors:

- Federal University of Latin-American Integration, 85867-970, Foz do Iguaçu-PR (Brazil)
- Federal University of Tocantins, 77804-970, Araguaína-TO (Brazil)

- Publication Date:

- OSTI Identifier:
- 22403379

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 348; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BRANES; BRIGHTNESS; COSMOLOGY; DISTURBANCES; GALAXIES; GRAVITATION; METRICS; NONLUMINOUS MATTER; PERTURBATION THEORY; ROTATION; SPACE-TIME; SPHERICAL CONFIGURATION; SYMMETRY

### Citation Formats

```
Capistrano, A.J.S., E-mail: abraao.capistrano@unila.edu.br, and Cabral, L.A.
```*Geometrical aspects on the dark matter problem*. United States: N. p., 2014.
Web. doi:10.1016/J.AOP.2014.05.013.

```
Capistrano, A.J.S., E-mail: abraao.capistrano@unila.edu.br, & Cabral, L.A.
```*Geometrical aspects on the dark matter problem*. United States. doi:10.1016/J.AOP.2014.05.013.

```
Capistrano, A.J.S., E-mail: abraao.capistrano@unila.edu.br, and Cabral, L.A. Mon .
"Geometrical aspects on the dark matter problem". United States. doi:10.1016/J.AOP.2014.05.013.
```

```
@article{osti_22403379,
```

title = {Geometrical aspects on the dark matter problem},

author = {Capistrano, A.J.S., E-mail: abraao.capistrano@unila.edu.br and Cabral, L.A.},

abstractNote = {In the present paper we apply Nash’s theory of perturbative geometry to the study of dark matter gravity in a higher-dimensional space–time. It is shown that the dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature of the standard cosmology. In order to test our model, we use a spherically symmetric metric embedded in a five-dimensional bulk. As a result, considering a sample of 10 low surface brightness and 6 high surface brightness galaxies, we find a very good agreement with the observed rotation curves of smooth hybrid alpha-HI measurements. - Highlights: • The metric perturbation and the embedding lead naturally to a “brane-world”-like higher dimensional structure. • Nash’s theorem as a cornerstone of the formation of geometrical structures. • The dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature. • A good agreement was found with the observed rotation curves of smooth hybrid alpha-HI measurements.},

doi = {10.1016/J.AOP.2014.05.013},

journal = {Annals of Physics (New York)},

issn = {0003-4916},

number = ,

volume = 348,

place = {United States},

year = {2014},

month = {9}

}