1998/11/24 by D. S. Salopek
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/16/1/022
published as Class.Quant.Grav. 16 (1999) 299-322 · 30 pages Latex (IOP) file with 2 IOP style files, to be published in Classical and Quantum Gravity (1998)
arxiv created 1998/11/24 · openalex publication_date 1999/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Strongly coupled gravitational systems describe Einstein gravity and matter in the limit that Newton's constant G is assumed to be very large. The nonlinear evolution of these systems may be solved analytically in the classical and semiclassical limits by employing a Green function analysis. Using functional methods in a Hamilton-Jacobi setting, one may compute the generating functional (`the phase of the wavefunctional') which satisfies both the energy constraint and the momentum constraint. Previous results are extended to encompass the imposition of an arbitrary initial hypersurface. A Lagrange multiplier in the generating functional restricts the initial fields, and also allows one to formulate the energy constraint on the initial hypersurface. Classical evolution follows as a result of minimizing the generating functional with respect to the initial fields. Examples are given describing Einstein gravity interacting with either a dust field and/or a scalar field. Green functions are explicitly determined for (1) gravity, dust, a scalar field and a cosmological constant and (2) gravity and a scalar field interacting with an exponential potential. This formalism is useful in solving problems of cosmology and of gravitational collapse.