The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics

Elliott Lieb, Horng Tzer Yau

Research output: Contribution to journalArticlepeer-review

201 Scopus citations

Abstract

Starting with a "relativistic" Schrödinger Hamiltonian for neutral gravitating particles, we prove that as the particle number N→∞ and the gravitation constant G→0 we obtain the well known semiclassical theory for the ground state of stars. For fermions, the correct limit is to fix GN2/3 and the Chandrasekhar formula is obtained. For bosons the correct limit is to fix GN and a Hartree type equation is obtained. In the fermion case we also prove that the semiclassical equation has a unique solution - a fact which had not been established previously.

Original languageEnglish (US)
Pages (from-to)147-174
Number of pages28
JournalCommunications In Mathematical Physics
Volume112
Issue number1
DOIs
StatePublished - Mar 1 1987

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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