Quantum gravity correction to Hawking radiation of the 2+1 dimensional wormhole
We carry out the Hawking temperature of a (2+1) dimensional circularly symmetric traversable wormhole in the framework of the generalized uncertainty principle (GUP). Firstly, we introduce the modified Klein-Gordon equation of the spin-0 particle, the modified Dirac equation of the spin-1/2 particle, and the modified vector boson equation of the spin-1 particle in the wormhole background, respectively. Given these equations under the Hamilton-Jacobi approach, we analyze the GUP effect on the tunneling probability of these particles near the trapping horizon, and subsequently, on the Hawking temperature of the wormhole. Furthermore, we have found that the modified Hawking temperature of the wormhole is determined by both wormhole's and tunneling particle's properties and indicated that the wormhole has a positive temperature similar to that of a physical system. This case indicates that the wormhole may be supported by ordinary (non-exotic) matter. In addition, we calculate the Unruh-Verlinde temperature of the wormhole by using Kodama vectors instead of time-like Killing vectors, and observe that it equals to the standard Hawking temperature of the wormhole.