Hawking Radiation Of Dirac Particles From5-dimensional Black Hole

In this thesis, we apply the quantum anomaly cancellation method andthe effective action approach as well as the method ofDamour-Ruffini-Sannan(DRS) to derive Hawking radiation of Dirac particles from five dimensional Godel and Myers-Perry black hole. We also investigate the Hawking black body spectrum of these black holes by using density matrix techniques.Using the dimensional reduction technique, we find that the fermionic field in the back-ground of the Godel and Myers-Perry black hole can be treated as an infinite collection of quantum fields in (1+1)-dimensional background coupled with the dilaton field and the U(1) gauge field near the horizon. In this two-dimensional reduction, as all the ingoing modes can not classically affect physics outside the horizon, the two-dimensional effective action in the exterior region becomes anomalous with respect to gauge or general coordinate symmetries. To cancel the anomaly, the Hawking flux is universally determined only by the value of anomalies at the horizon. Thus Hawking temperature and fluxes are found.Another method to correctly reproduce Hawking fluxes is based on the effective action which is induced from trace anomaly by using the covariant boundary condition and the co-variant gauge current as well as the covariant energy-momentum tensor. This approach is particularly direct and useful since one is able to obtain an expression for the currents and energy-momentum tensors directly by taking appropriate functional derivatives of the effective action.By comparison, we also calculate the Hawking temperature via the method of Damour-Ruffini-Sannan. The Hawking temperature obtained agrees with the surface gravity formula while the Hawking fluxes derived from the anomaly cancellation method and the effective ac-tion approach are in complete agreement with the ones obtained from integrating the Planck distribution. Finally, using density matrix techniques, we obtain the Hawking radiation spectrum of the Godel and Myers-Perry black hole. It is shown that the radiation spectrum is consistent with a perfect blackbody spectrum in the Hawking temperature.