# Tolman-Oppenheimer-Volkoff equations in the presence of the Chaplygin gas: Stars and wormholelike solutions

## Abstract

We study static solutions of the Tolman-Oppenheimer-Volkoff equations for spherically symmetric objects (stars) living in a space filled with the Chaplygin gas. Two cases are considered. In the normal case, all solutions (excluding the de Sitter one) realize a three-dimensional spheroidal geometry because the radial coordinate achieves a maximal value (the 'equator'). After crossing the equator, three scenarios are possible: a closed spheroid having a Schwarzschild-type singularity with infinite blueshift at the 'south pole', a regular spheroid, and a truncated spheroid having a scalar curvature singularity at a finite value of the radial coordinate. The second case arises when the modulus of the pressure exceeds the energy density (the phantom Chaplygin gas). There is no more equator and all solutions have the geometry of a truncated spheroid with the same type of singularity. We also consider static spherically symmetric configurations existing in a universe filled with only the phantom Chaplygin gas. In this case, two classes of solutions exist: truncated spheroids and solutions of the wormhole type with a throat. However, the latter are not asymptotically flat and possess curvature singularities at finite values of the radial coordinate. Thus, they may not be used as models of observable compact astrophysicalmore »

- Authors:

- Dipartimento di Scienze Fisiche e Mathematiche, Universita dell'Insubria, Via Valleggio 11, 22100 Como (Italy)
- (Italy)
- (Russian Federation)
- (France)

- Publication Date:

- OSTI Identifier:
- 21254145

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 78; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.78.064064; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ASTROPHYSICS; CONFIGURATION; COORDINATES; DE SITTER GROUP; ENERGY DENSITY; EQUATIONS; MATHEMATICAL SOLUTIONS; PHANTOMS; SINGULARITY; SPHERICAL CONFIGURATION; SPHEROIDS; STARS; SYMMETRY; THREE-DIMENSIONAL CALCULATIONS; UNIVERSE

### Citation Formats

```
Gorini, V., Moschella, U., Kamenshchik, A. Yu., Pasquier, V., Starobinsky, A. A., INFN, sez. di Milano, Via Celoria 16, 20133 Milano, Dipartimento di Fisica and INFN, Via Irnerio 46, 40126 Bologna, L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow, Service de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette, and L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow.
```*Tolman-Oppenheimer-Volkoff equations in the presence of the Chaplygin gas: Stars and wormholelike solutions*. United States: N. p., 2008.
Web. doi:10.1103/PHYSREVD.78.064064.

```
Gorini, V., Moschella, U., Kamenshchik, A. Yu., Pasquier, V., Starobinsky, A. A., INFN, sez. di Milano, Via Celoria 16, 20133 Milano, Dipartimento di Fisica and INFN, Via Irnerio 46, 40126 Bologna, L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow, Service de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette, & L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow.
```*Tolman-Oppenheimer-Volkoff equations in the presence of the Chaplygin gas: Stars and wormholelike solutions*. United States. doi:10.1103/PHYSREVD.78.064064.

```
Gorini, V., Moschella, U., Kamenshchik, A. Yu., Pasquier, V., Starobinsky, A. A., INFN, sez. di Milano, Via Celoria 16, 20133 Milano, Dipartimento di Fisica and INFN, Via Irnerio 46, 40126 Bologna, L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow, Service de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette, and L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow. Mon .
"Tolman-Oppenheimer-Volkoff equations in the presence of the Chaplygin gas: Stars and wormholelike solutions". United States.
doi:10.1103/PHYSREVD.78.064064.
```

```
@article{osti_21254145,
```

title = {Tolman-Oppenheimer-Volkoff equations in the presence of the Chaplygin gas: Stars and wormholelike solutions},

author = {Gorini, V. and Moschella, U. and Kamenshchik, A. Yu. and Pasquier, V. and Starobinsky, A. A. and INFN, sez. di Milano, Via Celoria 16, 20133 Milano and Dipartimento di Fisica and INFN, Via Irnerio 46, 40126 Bologna and L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow and Service de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette and L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow},

abstractNote = {We study static solutions of the Tolman-Oppenheimer-Volkoff equations for spherically symmetric objects (stars) living in a space filled with the Chaplygin gas. Two cases are considered. In the normal case, all solutions (excluding the de Sitter one) realize a three-dimensional spheroidal geometry because the radial coordinate achieves a maximal value (the 'equator'). After crossing the equator, three scenarios are possible: a closed spheroid having a Schwarzschild-type singularity with infinite blueshift at the 'south pole', a regular spheroid, and a truncated spheroid having a scalar curvature singularity at a finite value of the radial coordinate. The second case arises when the modulus of the pressure exceeds the energy density (the phantom Chaplygin gas). There is no more equator and all solutions have the geometry of a truncated spheroid with the same type of singularity. We also consider static spherically symmetric configurations existing in a universe filled with only the phantom Chaplygin gas. In this case, two classes of solutions exist: truncated spheroids and solutions of the wormhole type with a throat. However, the latter are not asymptotically flat and possess curvature singularities at finite values of the radial coordinate. Thus, they may not be used as models of observable compact astrophysical objects.},

doi = {10.1103/PHYSREVD.78.064064},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 78,

place = {United States},

year = {Mon Sep 15 00:00:00 EDT 2008},

month = {Mon Sep 15 00:00:00 EDT 2008}

}