Hawking Radiation: Derivation of Black-hole Tunneling as Bekenstein-Hawking Entropy BY M. A Lateef and E.O. Oyewande (PAGES 11-20)

**Abstract**

We present a mechanistic derivation of Hawking radiation, a black hole radiation, as a consequence of particle tunneling phenomenon through the event horizon of a black hole. This tunneling process radiates away the mass of the black hole (Hawking radiation), outwardly to infinity.The correction to the thermal spectrum is of precisely the form that one would expect from an underlying unitary quantum theory and this may have profound implications for the black hole information paradox.Up till now the correspondence between blackhole particle transmission coefficient and the Bekenstein-Hawking entropy has not been clearly established. This work tackles this issue and provides an alternative approach to clearly establish a correspondence between transmission coefficient of the positive energy particle and Bekenstein-Hawking entropy using appropriate relations and mathematical techniques.

Keywords: Hawking radiation, Black-hole tunneling, Bekenstein-Hawking entropy

Key Parameters:Φ= Massless scalar field in a Schwarzschild black hole space-time u= Constant phase T_H=T_∞ = Hawking temperature(temperature observed at infinity) κ= Surface gravity of the black hole T=Unruh temperature V= Redshift factor at the observer positions V_∞= Redshift factor at infinity V_2M= Redshift factor at the horizon Γ= Transmission coefficient (tunneling rate) S= Tunneling action a=Congruent acceleration M= Mass of the black hole r= Radius of the black hole ω_i=ithParticle energy ω= Particle energy A_S= Area of the black hole S_BH= Bekenstein-Hawking entropy t = Imaginary time p(r)=momentum of the particle u(r)= is used to define particle and is called single particle solution