A new touch temperature of the event horizon and Rindler horizon in the Kinnersley spacetime

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 $${\dot{r}}_H\ne 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mover> <mml:mi>r</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mi>H</mml:mi> </mml:msub> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . 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.

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