Quantum Stabilization of General-Relativistic Variable-Density Degenerate Stars

David Eric Cox, Ronald L. Mallett, MP Silverman

Department of Physics, Trinity College, Hartford, CT.
Department of Physics, University of Connecticut, Storrs, CT.

DOI: 10.4236/jmp.2012.37077                

Abstract

Research by one of the authors suggested that the critical mass of constant-density neutron stars will be greater than eight solar masses when the majority of their neutrons group into bosons that form a Bose-Einstein condensate, provided the bosons interact with each other and have scattering lengths on the order of a picometer. That analysis was able to use Newtonian theory for the condensate with scattering lengths on this order, but general relativity provides a more fundamental analysis. In this paper, we determine the equilibrium states of a static, spherically-symmetric variable-density mixture of a degenerate gas of noninteracting neutrons and a Bose-Einstein condensate using general relativity. We use a Klein-Gordan Lagrangian density with a Gross-Pitaevskii term for the condensate and an effective field for the neutrons. We show that a new class of compact stars can exist with masses above the Oppenheimer-Volkoff limit, provided the scattering length of the bosons is large enough. These stars have no internal singularities, obey causality, and demonstrate a quantum mechanism consistent with general relativity that could prevent collapsed stars from becoming black holes.

Keywords

Gravity; General Relativity; Neutron Stars; Black Holes; Bose-Einstein Condensates; Numerical Physics

Conflicts of Interest

The authors declare no conflicts of interest.

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