Application of local Poincare group in solving Dirac equation in the presence of dilaton black hole space-time and use of 3+1 formalism to calculate Hawking effect

Localized Poincare symmetry, leads to the Poincare gauge theory of gravity which contains GR as a special case. Using this localized symmetry, we solve the Dirac equation in the presence of curved space-time around a dilaton black-hole(1). The solution of Dirac equation concludes wave equation for four-component Dirac- spinor which describes the movement of fermions around a dilaton black-hole. Using wave equation and ADM mass (2), as well as 3+1 formalism, we calculate Hawking effect as well as temperature and entropy for dilaton black-hole.