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Anisotropic stars: Exact solutions. (English) Zbl 1014.83015
Summary: We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound objects. We consider the full general-relativistic treatment of this problem and obtain exact solutions for various forms of the equation of state connecting the radial and tangential pressures. It is shown that pressure anisotropy can have significant effects on the structure and properties of stellar objects. In particular, the maximum value of \(2M/R\) can approach unity \((2M/R < 8/9\) for isotropic objects) and the surface redshift can be arbitrarily large.

MSC:
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
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