Semi-relativistic stability and critical mass of a system of spinless bosons in gravitational interaction

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The N particle hamiltonian Σi=1N(pi2+m2)1/2-Σi=4(3√3 Gm)-1 ~ 0.77(Gm)-1, consistent with the bound Mcr<1.51 (Gm)-1 obtained by one of us (A.M.). Comparison with the Kaup-Ruffini-Bonazzola statistical curved space Klein-Gordon equation result Mcr~0.633 (Gm)-1 raises interesting questions.
On leave from the Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India.

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