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Effect of pressure anisotropy on Buchdahl-type relativistic compact stars. (English) Zbl 1429.83028
Summary: We consider exact models for dense relativistic stars with anisotropic pressures and containing Buchdahl-type spacetime geometry. The Buchdahl condition can be transformed to an Euler-Cauchy equation for the gravitational potentials. We solve this condition to find a new exact solution to the Einstein field equations with anisotropic matter distribution. We show that the exact solution produces a realistic model of a compact relativistic star satisfying all physical requirements. The regularity, equilibrium, causality, stability, energy conditions and compactness limits for a well behaved compact sphere are satisfied.
MSC:
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C15 Exact solutions to problems in general relativity and gravitational theory
85A15 Galactic and stellar structure
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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