Rotational metric: a solution to Einstein's clock-rate problem and its magnetospheric applications*

Abstract The rotational metric provides an exact solution to Einstein's clock-rate problem in curved spacetime, specifically, whether time flows more slowly at the equator of a compact object such as a neutron star than at its poles. It features a curvature singularity, an event horizon, a potentially evolving ergosphere, a rigidly-rotating normal space, and two stationary limit surfaces. Although derived from the Schwarzschild metric through rotational transformations, it includes an additional ergosphere. Given the equivalence of inertia and gravity, this demonstrates how non-inertial transformations, such as rotational transformations, can introduce new spacetime structures into a gravitational system. In particular, the additional physical degrees of freedom carried by rotational transformations are eaten by the gravitational system to form an additional ergosphere. Furthermore, the rotational metric effectively models a rigidly-rotating gravitational system and is applicable for describing rotationally-induced gravitational effects in various rotating magnetospheres.