A Role of the Uncertainty Principle in General Relativity and the Limiting Size of Collapsing Fermion Spheres

概要

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An attempt is made to modify the Schwarzschild metric by the uncertainty principle in space regions of the linear size of the order of the Planck length L^*=(h^^-G/c^3)^<1/2>〜10^<-33> cm, and the role of the modified metric in avoiding the unlimited gravitational collapse of superdense Fermion spheres is examined. It is seen that the effect of the uncertainty principle is to introduce, at the center of symmetry of the system, a "repulsive hole" in which the matter is energetically unstable against the escape to outer regions. The radius of this hole for a system of mass M and radius R is seen to be L^*(R/R_<gr>)^<1/2>, where R_<gr>=2GM/c^2 is the gravitational radius associated with the mass M. The limiting radius and mass of the collapsing extreme relativistic Fermi gas are roughly given by N^<2/5>L^* and N^<2/5>m^*, respectively, where N is the number of particles in the gas and m^*=h^^-/_<c>L^*=(h^^-/G)^<1/2>〜10<-5> g is the Planck mass.
理論物理学刊行会の論文
1971-09-25