Abstract
In this paper, the quantum tunneling of the non-stationary Kerr-Newman black hole is investigated via Hamilton-Jacobi equation and two types of general tortoise coordinate transformations. The tunneling rates, the Hawking temperatures and radiation spectrums are derived respectively. Our result shows that the new type of general tortoise coordinate transformation is more reasonable.
Highlights
In 1974, Hawking proved black holes can emit thermal radiation by the view of quantum theory [1]
The case of higherdimensional space-time and Finsler black holes is referred in [16,17,18], which shows that the quantum tunneling is a helpful method for us to understand the origin of Hawking radiation
Contrast formula Γ = exp(−βE) with Eq (34), where β is inverse temperature on the horizon, and the E is the energy of tunneling particle, it is clear to know that the Hawking temperature is depends constant α(ν0, θ0)
Summary
In 1974, Hawking proved black holes can emit thermal radiation by the view of quantum theory [1]. According to Palnevé coordinate transformations and WKB approach, the tunneling rate of particles from inside to outside of horizon can be written as Γ ∝ exp(−2 Im I ) [6] Along with this method, people have studied thermodynamic property of stationary black holes [7,8,9,10,11]. It is well known that the horizon of nonstationary black holes varies with the time, so, there are some problems when studying the Hawking radiation of non-stationary black holes To solve these problems, people usually introduce the general tortoise coordinate transformation combining with the method of Damour-Ruffini. The Hamilton-Jacobi equation was being derived from Klein-Gordon equation the tunneling radiation of non-stationary Kerr-Newman black hole was studied via the new type of general tortoise coordinate.
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