General Relativity and Gravitation

, Volume 22, Issue 8, pp 925–946 | Cite as

Solutions for static gas spheres in general relativity

  • Henning Knutsen
Research Articles

Abstract

A method for constructing solutions for a relativistic static “gaseous” sphere is examined. “Gaseous” here means that the densityρ vanishes at the outer boundary together with the pressurep. Two different classes of solutions are investigated in detail. The models of both these classes have the property that the density gradient is zero both at the center and at the surface. It is further shown that both classes yield models which are physically acceptable, i.e. both the pressure and the density are positive and finite inside the outer boundary of the sphere, and their respective gradients are negative. The trace of their energy-momentum tensors are positive, and the adiabatic sound speeds are decreasing outwards throughout the sphere. The relativistic adiabatic indices are examined, and it is found that they are decreasing functions of radial coordinate. It is shown that for the first class this index is 3/2 at the surface, while for the second class it is 4/3 at the boundary. We find that the models of the first class arestable with respect to small radial disturbances. Putting the density at the center equal to 1016g cm−3, the maximum mass for the stable class is found to be 0.87 solar masses.

Keywords

General Relativity Density Gradient Differential Geometry Outer Boundary Sound Speed 

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Henning Knutsen
    • 1
  1. 1.Rogaland University CentreUllandhaugNorway

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