Reconnection of Gravitational Fields

In a tetrad formulation of general relativity, an ideal Ohm-type condition for the gravitational field implies the conservation of gravitational fluxes and the preservation of the connectivity of gravitational field sheets. We investigate the consequences of departures from ideal gravitational evolution by developing a theory of gravitational reconnection, defined as a change in the connectivity of gravitational field sheets arising from the breakdown of the ideal frozen-in evolution of the gravitational field. We derive quantitative measures of the gravitational reconnection rate, show that gravitational reconnection alters the energy-momentum exchange between the gravitational and matter sectors, and determine how it modifies the evolution of gravitational helicity. Our results provide a quantitative framework for describing changes in gravitational connectivity and their consequences in dynamical spacetimes.