Constructing physically valid fluid spheres in general relativity

Details Constructing physically valid fluid spheres in general relativity Constructing physically valid fluid spheres in general relativity

Jul 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991gregr..23..843k&link_type=abstract

General Relativity and Gravitation, Volume 23, Issue 7, pp.843-859

Computer Science

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Scientific paper

We extend a method by Goldman to include conditions which are both necessary and sufficient for construction of physically acceptable relativistic fluid spheres. We thus give the conditions for having finite and non-negative pressure and finite and positive density inside the fluid sphere. We also give conditions for the pressure gradient and the density gradient to be negative and for the speed of sound to be less than the speed of light in vacuum. We further give the condition for the trace of the energy-momentum tensor to be positive and for the relativistic adiabatic index to be larger than 4/3. A model given by Goldman is examined, and we find that all these conditions are fulfilled. We further show that this model is stable. However, we also give a class ofnew exact solutions, and show that these models are physically valied. These models are also stable with respect to small radial disturbances. We calculated the total mass, the density and the physical radius for these fluid spheres. Some of these spheres turn out to be extremely compact. They can have a radius of only several centimeters, but typically contain the mass of a planet. We put these models forward as tentative exact solutions for spheres which could contain the hidden dark matter in the universe.

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