A maximally-constrained scheme for 3+1 numerical relativity is described using maximal slicing and spherical tensor components. Thanks to the
additional introduction of a flat 3-metric on spatial hypersurfaces,corresponding to their asymptotic structure, it is possible to
generalize the Dirac gauge to spherical coordinates. Thus, the Einstein equations can be written as a coupled system of five elliptic
equations (including Hamiltonian and momentum constraints) and two scalar wave equations,which correspond to the dynamical degrees of
freedom of the gravitational field. High-precision numerical models of rotating relativistic stars and evolution of 3D gravitational wave spacetime are presented as numerical examples. In particular, the
accuracy of the resolution of the constraints equations is shown, as well as that of the evolution equations which are not actually
solved.
Copyright. All Rights Reserved.