WIGHTMAN FUNCTIONS BEHAVIOR ON THE EVENT HORIZON OF AN EXTREMAL REISSNER-NORDSTROM BLACK-HOLE

A weaker Haag, Narnhofer and Stein (HNS) prescription and a weaker Hes sling quantum equivalence principle for the behaviour of thermal Wight man functions on an event horizon are analysed in the case of an extre mal Reissner-Nordstrom black hole in the limit of large mass. In order to avoid the degeneracy of the metric in the stationary coordinates o n the horizon, a method is introduced which employs the invariant Leng th of geodesics which pass the horizon. First the method is checked fo r a massless scalar field on the event horizon of the Rindler wedge, e xtending the original procedure of Haag et al onto the whole horizon a nd recovering the same results found by Hessling. The HNS prescription and Hessling's prescription for a massless scalar field are then anal ysed on the whole horizon of an extremal Reissner-Nordstrom black hole in the limit of large mass. It is proved that the weak form of the HN S prescription is satisfied for all finite values of the temperature o f the KMS states, i.e. this principle does not determine any Hawking t emperature. It is found that the Reissner-Nordstrom vacuum, i.e. T = 0 , does satisfy the weak HNS prescription and it is the only state whic h also satisfies Hessling's weak prescription. Finally, it is suggeste d that all the previously obtained results should still be valid if th e requirements of a massless field and of a large-mass black hole are also dropped.