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We present a new application of the Regge-Teitelboim method for treatingsymmetries which are defined asymptotically. It may be regarded ascomplementary to the one in their original 1974 paper. The formulation is basedon replacing an asymptotic plane by the two--sheeted ``hourglass" shapedsurface obtained by joining smoothly an incoming hyperboloid with an outgoingone. The hyperboloids have a fixed radius, and as one moves the center of thehourglass along the time axis one covers the whole of spacetime. The motivationis to study radiation, and the hourglass is well suited to the task because itis asymptotically null, and thus is able to register the details of theprocess. A simple parity condition for the fields on the hyperboloid is given.It specifies that as much radiation as is coming in as it is going out. Withit, a Hamiltonian formulation of the symmetry of Bondi, van der Burg, Metznerand Sachs is developed fir both electromagnetism and gravitation. It isindispensable for the construction to have electric--magnetic dualityasymptotically. For gravitation, a formulation for the linearized theory on thehourglass has not been explicitly constructed; but enough rudiments of it aregiven so that the main results can be established. A definition for angularmomentum wish is conserved (for which the ``magnetic sector'' is essential) isgiven. It incorporates an interrelationship between spin and charge. For thegravitational field, Taub-NUT space appears as the analog of a magnetic pole.

Regge-Teitelboim analysis of the symmetries of electromagnetic and gravitational fields on asymptotically null spacelike surfaces