Axially symmetric,uniformly rotating neutron stars in general relativity: a non-perturbative approach

The equilibrium problem for an axially symmetric, uniformly rotating, elastic solid neutron star is considered within the framework of a new formulation of relativistic elasticity. The analysis is fully relativistic and free of any assumption about the existence of a globally relaxed state of the star. Static configurations may exist only for rigid motions, and for such motions a set of six Einstein equations for six variables is proposed. Due both to the importance of elastic-solid lattices for the structure of neutron stars crusts and to the lack, up to now, of satisfactory axially symmetric perfect fluid interior solutions matching an asimpotically flat exterior, the results seem to indicate the possibility of constructing physically valid models of axially symmetric astrophysical objects in general relativity. The particular case of non-rotating axially symmetric elastic sources is also discussed.