Tunneling radiation of fermions with 1/2 and 3/2 spins from a charged axisymmetric nonstationary black hole

In this paper, we derived Hamilton–Jacobi equation for spin 1/2 and 3/2 fermions from Dirac equation and Rarita–Schwinger equation. Then, by using the Hamilton–Jacobi equation and general tortoise coordinate transformation, the tunneling rate and Hawking temperatures of a nonstationary axisymmetric symmetry black hole are investigated. The result shows that the tunneling rate, temperature and surface gravity are all related to the properties of horizons of the black hole, the cosmological constant [Formula: see text], the charge [Formula: see text], mass of black hole [Formula: see text] and the Eddington time [Formula: see text].

TORTOISE COORDINATE TRANSFORMATION ON APPARENT HORIZON OF A DYNAMICAL BLACK HOLE

Thinking of Hawking radiation calculation from a Schwarzschild black hole using Damour-Ruffini method, some key requirements of the tortoise coordinate transformation are pointed out. Extending these requirements to a dynamical black hole, a dynamical tortoise coordinate transformation is proposed. Under this new dynamical tortoise coordinate transformation, Hawking radiation from a Vaidya black hole can be got successfully using Damour-Ruffini method. Moreover, we also find that the radiation should be regarded as originating from the apparent horizon rather than the event horizon at least from the viewpoint of the first law of thermodynamics.

Hawking radiation from a dynamical Kerr–Newman black hole

After Hawking radiation from a Schwarzschild black hole is calculated using the Damour–Ruffini method, the tortoise coordinate transformation in a static black hole is extended to a dynamical axisymmetric black hole, such as a dynamical Kerr–Newman black hole. Under the generalized tortoise coordinate transformation, Hawking radiation from a dynamical Kerr–Newman black hole is obtained successfully. Moreover, it also seems to occur on the apparent horizon instead of the event horizon.