The Newtonian limit of geometrostatics

index notation, 7, 88acceleration, 73, 74achronal, 19ADM-mass, 25affine connection, 9analytic at infinity, 49associated 1-from, 95associated H-tensor field, 95asymptotically flat, 22, 23, 40asymptotically flatmanifold, 23asymptotically Schwarzschildian, 28asymptotically spherically round, 28 Bianchi identityfirst, 10second, 34, 92bounded away from infinity, 23 Cartan connection, 9Cartesian coordinates, 98Cauchy problem, 19, 21Cauchy surface, 19causality constant, 90center of gravity, 26center of mass, 26, 27, 61, 68, 71center of massADM, 27asymptotic, 43CMC, 28Huisken-Yau, 28intrinsic, 30Newtonian, 68physical, 61pseudo-Newtonian, 68, 109Christoffel symbols, 5chronal future, 19CMC-surface, 28Codazzi equation, 8CoM, 26conformally transformed metric, 35connectionaffine, 9Levi-Cività, 5symmetric, 9torsion free, 9conservation of matter equation, 91constraintenergy, 20Hamiltonian, 20momentum, 20convergencepointwise, 101uniform, 101, 102coordinatesasymptotically flat, 23at infinity, 23harmonic, 7isotropic, 36wave harmonic, 7, 99cotangent bundle, 5curvatureendomorphism, 6, 9extrinsic, 20Ricci, 6scalar, 6 decay rate, 23defect tensor, 95development, 21developmentglobally hyperbolic, 21maximal, 21distribution, 8, 32distributioninvolutive, 8tangent, 8