Black Hole Radiance and Supersymmetry

Starting with free massless scalar and spinor fields described by a globally N = 1 supersymmetric action, infalling on a Schwarzschild black hole, the outgoing Hawking radiation is shown to break supersymmetry spontaneously, exactly as induced by a heat bath in Minkowski space, with no generation of Nambu-Goldstone fermions. Bose-fermi asymmetry appears to be intrinsic to the formulation of singularity theorems in general relativity [1]. The weak energy condition is certainly not valid for spinor fields, while for classical bosonic particles it is perfectly consistent with phenomena like the Penrose process [2]. Perhaps for related reasons, this dissimilarity persists through quantization of the respective matter fields in classical black hole spacetimes. Indeed, superradiance of spin-1/2 particles is severely suppressed, in contrast to integral spin fields of appropriate charge/angular momentum [3]. Furthermore, in Hawking’s celebrated theory of black hole evaporation [4], integral spin fields are radiated in a Planckian (Bose-Einstein) spectrum at a ‘temperature’ proportional to the surface gravity of the black hole. Spinor fields, on the other hand, are radiated in accord with Fermi-Dirac statistics at the same temperature. Of course, one can scarcely overemphasize that this ‘thermal’ nature of the Hawking spectrum has no obvious statistical mechanical underpinning, in contrast to standard thermodynamics; it is ∗email: [email protected]