Abstract Starting from the symplectic potential for the -Palatini--Holst action on a null hypersurface, we identify an auxiliary conformal field theory (CFT), which carries a representation of the constraint algebra of general relativity on a null surface. The radiative data, which is encoded into the shear of each null generator, is mapped into an SU (1, 1) current algebra on each light ray. We study the resulting quantum theory for both bosonic and fermionic representations. In the fermionic representation, the central charge on each null ray is positive, for bosons it is negative. A negative central charge implies a non-unitary CFT, which has negative norm states. In the model, there is a natural SU (1, 1) Casimir. For the bosonic representations, the SU (1, 1) Casimir can have either sign. For the fermionic representations, the SU (1, 1) Casimir is always greater or equal to zero. To exclude negative norm states, we restrict ourselves to the fermionic case. To understand the physical implications of this restriction, we express the SU (1, 1) Casimir in terms of the geometric data. In this way, the positivity bound on the SU (1, 1) Casimir translates into an upper bound for the shear of each null generator. In the model, this bound must be satisfied for all three-dimensional null hypersurfaces. This in turn suggests to apply it to an entire null foliation in an asymptotically flat spacetime. In this way, we obtain a bound on the radiated power of gravitational waves in the model.
Wolfgang Wieland (Tue,) studied this question.