Abstract
The quantum gravity correction to the Hawking temperature of the 2+1 dimensional spinning dilaton black hole is studied by using the Hamilton-Jacobi approach in the context of the Generalized Uncertainty Principle (GUP). It is observed that the modified Hawking temperature of the black hole depends on both black hole and the tunnelling particle properties. Moreover, it is observed that the mass and the angular momentum of the scalar particle have the same effect on the Hawking temperature of the black hole, while the mass and total angular momentum (orbital+spin) of Dirac particle have different effect. Furthermore, the mass and total angular momentum (orbital+spin) of vector boson particle have a similar effect that of Dirac particle. Also, thermodynamical stability and phase transition of the black hole are discussed for scalar, Dirac and vector boson in the context of GUP, respectively. And, it is observed that the scalar particle probes the black hole as stable whereas, as for Dirac and vector boson particles, it might undergoes second-type phase transition to become stable while in the absence of the quantum gravity effect all of these particle probes the black hole as stable.
Statistical entropy of a stationary dilaton black hole from the Cardy formula
