The Momentum Constraints of General Relativity and Spatial Conformal Isometries
نویسنده
چکیده
Transverse–tracefree (TT–) tensors on (R, gab), with gab an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall–off at infinity, TT tensors allow a multipole–type expansion. When gab has no conformal Killing vectors (CKV’s) it is proven that any finite but otherwise arbitrary set of moments can be realized by a suitable TT tensor. When CKV’s exist there are obstructions — certain (combinations of) moments have to vanish — which we study. MSC numbers: 83C05, 83C40 *) Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P9376–PHY.
منابع مشابه
Initial Data for General Relativity with Toroidal Conformal Symmetry Typeset Using Revt E X
A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a U (1) × U (1) group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, t...
متن کاملInitial Data with Toroidal Conformal Symmetry
A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a U(1) × U(1) group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, the...
متن کاملCanonical General Relativity: the Diffeomorphism Constraints and Spatial Frame Transformations
Einstein’s general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric and spatial vielbein as canonical coordinates. This results in a Hamiltonian in standard form that consists of Hamiltonian and momentum constraints as well as...
متن کاملCERN–TH/97–168 gr-qc/9707039 CANONICAL GENERAL RELATIVITY: THE DIFFEOMORPHISM CONSTRAINTS AND SPATIAL FRAME TRANSFORMATIONS
Einstein’s general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric and spatial vielbein as canonical coordinates. This results in a Hamiltonian in standard form that consists of Hamiltonian and momentum constraints as well as...
متن کاملar X iv : g r - qc / 0 50 10 24 v 1 8 J an 2 00 5 Conformal geometrodynamics
The standard geometrodynamics is reformulated into a theory of conformal geometrodynamics by extending the ADM phase space for canonical general relativity to a phase space consisting of York’s exterior mean curvature time, conformal 3-metric and their momenta. Accordingly, an additional constraint is introduced, called the conformal constraint. In terms of the new canonical variables, a diffeo...
متن کامل