Particle Tunnels From Garfinkle–horne Black Hole and Horowitz–strominger Black Hole

Abstract

When the black hole radiates particles, it losses energy and shrinks, it is the contraction of the horizon that sets the tunnelling barrier. This article extents the work of M. Parikh to GH black hole and HS black hole. Applying WKB approximation, we calculate the rate of Hawking radiation and found that the rate of tunnelling equals precisely the exponent of the difference of the entropy of the black hole before and after emission. We also obtain the result that the energy spectrum of radiation deviates from the exact thermality.

Massive Uncharged and Charged Particles' Tunneling From the Horowitz–strominger Dilaton Black Hole

“…But our result shows that their emission rates are also consistent with the unitary theory, the same as that of the case of massless particles' tunneling, which manifests that the conclusion is independent of the kind of particles. On the other hand, as is seen from the Refs [13,21], for the massless particles' tunneling of the H.S Dilaton black hole, the authors do directly calculate the imaginary part of the action after doing the r integral, and this direct calculation is usually complex. However, in our paper, we simplify the calculation.…”

“…Thus, when we consider the massive uncharged or charged particles tunneling across the event horizon without the angle momentum, the equations corresponding to (24) are just respectively the (14) and the (21). Moreover, in Refs [13,21], we can also obtain the corresponding equation from (24).…”

“…Moreover, in Refs [13,21], we can also obtain the corresponding equation from (24). It implies that not only our simplified calculation has hidden the laws of black hole thermodynamics, but also all those methods (either the original Parikh and Wilczek's method or its extended method) have the underlying relationship with the laws of black hole thermodynamics.…”

Massive Particles' Hawking Radiation via Tunneling From the G.H. Dilaton Black Hole

“…In order to calculate (21) conveniently, we can change the variant M into r H [10,13], which we can get from (2) (3)…”

“…However, the particles which they have treated all are massless and follow the radial lightlike geodesics when they tunnel across the horizon, while the massive particles don't follow the radial lightlike geodesics. In this paper, we extend Parikh's method to a particular black hole solution-G.H Dilaton black hole [10], and investigate the massive particles' tunneling [5,6]. Then, we calculate the emission rate at the event horizon of the G.H Dilaton black hole.…”