Abstract
The Kinnersley spacetime not only describes a non-spherical symmetric, non-stationary and accelerating black hole, but also can be used to explore the characteristics of collision of two black holes because it has two horizons: the Rindler horizon and the event horizon. Previous research shows Rindler horizon and the event horizon cannot touch due to violation of the third law of thermodynamics. By solving a fermion dynamical equation including the Lorentz dispersion relation, we obtain a modified radiation temperature at the event horizon of the black hole, as well as the colliding temperature at the touch point of Rindler horizon and the event horizon. We find the temperature at the touch point is not equal to zero if {dot{r}}_Hne 0. This result indicates that the event horizon and Rindler horizon can collide without violation of the third law of thermodynamics when Lorentz dispersion relation is considered.
Highlights
Dynamical black holes are those whose mass, charge, or angular momentum evolves with time
As an extension of the Vaidya metric [1], the Kinnersley spacetime [2] describes a dynamical black hole that accelerates in recoil
For all of the studies regarding Hawking radiation before 2000, one had ignored the energy loss of black holes and the contraction of the radius of the event horizon caused by particle radiation
Summary
Dynamical black holes are those whose mass, charge, or angular momentum evolves with time. For all of the studies regarding Hawking radiation before 2000, one had ignored the energy loss of black holes and the contraction of the radius of the event horizon caused by particle radiation. Wilczek et al further considered the energy conservation in the study of black hole tunneling radiation. They demonstrated that the mass of the black hole would decrease as the radiation takes place. As a result, it leads to the contraction of the black hole radius, which causes the appearance of the potential barrier.
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