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

Abstract

The N particle hamiltonian Σ_i=1^N(p_i²+m²) ^½−Σ_i<j≤NGm²/r_ij implies a critical mass M_cr a bosonic analogue of the Chandrasekhar limit, beyond which there must be relativistic collapse. We prove that M_cr≥4(3√3 Gm)⁻¹∼0.77(Gm)⁻¹, consistent with the bound M_cr<1.51 (Gm)⁻¹ obtained by one of us (A.M.). Comparison with the Kaup-Ruffini-Bonazzola statistical curved space Klein-Gordon equation result M_cr≈0.633 (Gm)⁻¹ raises interesting questions.