Topics in the Dynamics or General Relativity
Arthur E. Fischer, Jerrold Eldon Marsden · CaltechAUTHORS (California Institute of Technology) · 1979
These notes co'-er several interrelated topics in the dynamics of general relathity.The main thrust is to present informally the Hamiltonian approach of Dirac [1,2) and of Arnow-itt, Deser and Misner [3] in a neW" W"ay and to investiga.tethe results W"hich can be obtained from this approach.WOe "Wl'ite the e.olution equations in the compact Hamiltonian formwhere J=( 0 1), -I ~ o} },.= lapse function, X = shift vector field, g = 3-metric on a space like hyper-Surface, :r = conjugate momentum and tP(g, n) = (Jt'(g, n),J(g, n») = 0 are the constraint equations.This form of the equations is useful in understanding the Hamiltonian structure of the evolution equations, their relationship to the linearized constraint equations, recent splittings of Moncrief [4] and the space of true gra>itational degrees of freedom.Consideration of the map DtP(g, n)•, the LI-adjoint of the derivative of (/) at (g, ;or), first arose in the authors' investigations of linearization stability of Einstein's equations [5,6], i.e. in the validity of first-order perturbation analysis.This and Monctief's beautiful contributions [4, 7] are presented in sect.5 and 6.The presence of the matrix J in the equations and indeed their Hamiltonian (.)