Inertial effects in the gravitational collapse of a rotating shell

Abstract

Inertial dragging effects of slowly rotating masses in asymptotically flat spaces are well known for the case of a stationary distribution of matter. In the present work we investigate a more general example in which angular acceleration of the matter is present. We solve the Einstein field equation for the case of the free-fall collapse of a rotating dust shell. The solution is exact, through terms of first order in $\ensuremath{\omega}$ (the angular velocity of the shell), for shells of arbitrary rest mass and radial velocity. The inertial properties of the flat interior region of this solution are discussed. Among the problems elucidated by this solution is the question of whether the inertial effects are instantaneous or retarded as viewed from infinity.