We investigate all shear-free perfect fluid solutions of the Einstein field equations where the pressure and energy density satisfy a (Formula presented.)-law equation of state with (Formula presented.). We prove that such a fluid is either non rotating or non expanding. As a consequence, it follows by combining our result with those of Collins and Wainwright that any such shear-free perfect fluid which models either an expand universe or a collapsing star must in fact be a Friedmann–Robertson–Walker spacetime.
Field of Research
0105 Mathematical Physics 0206 Quantum Physics 0201 Astronomical And Space Sciences 010504 Mathematical Aspects of General Relativity 010207 Theoretical and Applied Mechanics
Socio Economic Objective
970101 Expanding Knowledge in the Mathematical Sciences
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