Matching slowly rotating spacetimes split by dynamic thin shells

We investigate within the Darmois-Israel thin shell formalism the match of neutral and asymptotically flat, slowly rotating spacetimes (up to the second order in the rotation parameter) when their boundaries are dynamic. It has several important applications in general relativistic systems, such as black holes and neutron stars, which we exemplify. We mostly focus on stability aspects of slowly rotating thin shells in equilibrium and surface degrees of freedom on the hypersurfaces splitting the matched slowly rotating spacetimes, e.g., surface energy density and surface tension. We show that the stability upon perturbations in the spherically symmetric case automatically implies stability in the slow rotation case. In addition, we show that when matching slowly rotating Kerr spacetimes through thin shells in equilibrium, surface degrees of freedom can decrease compared to their Schwarzschild counterparts, meaning that energy conditions could be weakened. Frame-dragging aspects of the match of slowly rotating spacetimes are also briefly discussed.