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Title: 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 » objects.« less

Authors:
; ; ; ;  [1];  [2];  [2];  [3];  [4];  [3]
  1. Dipartimento di Scienze Fisiche e Mathematiche, Universita dell'Insubria, Via Valleggio 11, 22100 Como (Italy)
  2. (Italy)
  3. (Russian Federation)
  4. (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. 2008. "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 = 2008,
month = 9
}
  • We investigate the Tolman-Oppenheimer-Volkoff equations for the generalized Chaplygin gas with the aim of extending the findings of V. Gorini, U. Moschella, A. Y. Kamenshchik, V. Pasquier, and A. A. Starobinsky [Phys. Rev. D 78, 064064 (2008)]. We study both the standard case, where we reproduce some previous results, and the phantom case. In the phantom case we show that even a superluminal group velocity arising for {alpha}>1 cannot prevent the divergence of the pressure at a finite radial distance. Finally, we investigate how a modification of the generalized Chaplygin gas equation of state, required by causality arguments at densitiesmore » very close to {lambda}, affects the results found so far.« less
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  • We investigate spherically symmetric perfect-fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the Misner-Sharp mass and to a function of the pressure that we introduce and that generalizes the Tolman-Oppenheimer-Volkoff equilibrium condition. We find that surfaces fulfilling those two conditions fit, locally, the requirements of a dividing shell, and we argue that cosmological initial conditions should allow its global validity. We analyze the particular cases of the Lemaitre-Tolman-Bondi dust models with amore » cosmological constant as an example of a cold dark matter model with a cosmological constant ({Lambda}-CDM model) and its generalization to contain a central perfect-fluid core. These models provide simple but physically interesting illustrations of our results.« less
  • Motivated by the recent questioning of the inverse-square law, the influence of short-range effects on the structure of a neutron star is presently investigated. This is analyzed by introducing an additional scalar (vector) massive field into the Oppenheimer-Volkoff formalism, which gives rise to a new attractive (repulsive) effect between the neutrons. This can be viewed as a simple modification of the equation of state. When phenomenologically acceptable parameters are used, the resulting effects on the star structure are unobservable. 11 refs.