The possibility of negative gravitational energy

The status and physical importance of the question “Can the energy of gravitational fields be negative?” is discussed. To study this question further a particular model of a gravitational shock wave has been developed. The energy corresponding to this model is a scalar functional of the two-geometry of the shock front. Values of the energy for special choices of the shock front have been calculated. These cases all give rise to positive energy, the energy becoming more positive as the shock front becomes more curved. However, no general proof is known to show that the energy is positive for all choices of two-geometries.