Absorption Cross Section Of Static EMDA Black Hole For Dirac And Scalar Particles

Studying wave scattering and absorbing in the black hole spacetimes is crucialto the understanding of the information of the black hole. Interest in the absorptionof quantum waves by black holes was reignited in the 1970s. Recently, study of theabsorption cross section in the context of higher-dimensional string theories attractmuch attention. Superstring theory springing up in recent years is still the onlyknown self-consistent theory which can quantize the gravity and unify the gravity,the electromagnetic interaction, the weak interaction and the strong interaction.This theory can explain the cosmic genesis and evolution, and may address the someopen questions of modern physics. The dilaton spacetimes in string theory havequalitatively different properties from those appearing in general relativity becauseof the appearance of dilaton, and so many author have focus their attentions oninvestigations of the spacetimes of dilaton black hole. One of the interesting topicis to study the scattering and absorbing of the particles in dilation spacetimes.In this paper, we will calculate the absorption cross section of the static EMDAblack hole for Dirac fermion particles and massive scalar particles by using theUnruh's method that matching the near-horizon wave radial solution and the as-ymptotic solution via the solution in the intermediate regime. It is shown that theabsorption cross section for massive scalar particles is (2M(2M-2D)~2(2π)~2(1+v~2)w)／(v~2(1-exp[-π(2M-2D)_ω(1+v~2)/v]))·When v≥2πMm, the cross section becomes (8πM(2M-2D))／v, which is the monotonydecrease function of v. We also find that the absorption cross section of EMDAblack hole depend very strong on the value of dilation D. As the increase of theabsolute values of dilation D, the absorption cross section decrease. However, forthe massless scalar particles at low energies the absorption cross section becomes8πM(2M-2D), which equals to the horizon area of a EMDA black hole. We knewthat the absorption cross section is equal to the horizon area for the Schwarzschildblack hole. Our result shows that this interesting property may be extend to theEMDA black hole.For Dirac particles, using similar method of computing the absorption crosssection of scalar particles, we find that the ratio of the low-energy absorption crosssection for Dirac fermion to that for minimally coupled scalar is 1/8, which is the same as the result of the Schwarzschild black hole.