Analysis of the cosmological Oppenheimer-Volkoff equations

Details Analysis of the cosmological Oppenheimer-Volkoff equations Analysis of the cosmological Oppenheimer-Volkoff equations

Aug 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000jmp....41.5582w&link_type=abstract

Journal of Mathematical Physics, Volume 41, Issue 8, pp. 5582-5597 (2000).

Mathematics

Mathematical Physics

2

Einstein-Maxwell Spacetimes, Spacetimes With Fluids, Radiation Or Classical Fields, Exact Solutions, Relativity And Gravitation, Particle-Theory And Field-Theory Models Of The Early Universe

Scientific paper

We formulate the Oppenheimer-Volkoff equations with nonzero cosmological constant, Λ. We analyze the behavior of solutions (under mild assumptions on the equation of state). We prove that solutions of the cosmological Oppenheimer-Volkoff equations are either singularity-free or else M(r)<0 for some r>0. [Here M(r) represents the total mass inside radius r.] We show that this behavior is independent of the magnitude of Λ when Λ<=0. In the case where Λ>0, we show that these conclusions hold provided that the solution is contained within a ball of radius 1/Λ. We prove that if M(r)<0 for some r>0 then the pressure tends to infinity before r=0.

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