ar X iv : h ep - t h / 03 11 03 6 v 3 4 F eb 2 00 4 Absorption Cross Section for S - wave massive Scalar

We examine the absorption cross section of the massive scalar field for the higher-dimensional extended object. Adopting the usual quantum mechanical matching conditions between the asymptotic and near-horizon solutions in radial equation, we check whether or not the universal property of the absorption cross section, which is that the low-energy cross section is proportional to the surface area of horizon, is maintained when the mass effect is involved. It is found that the mass effect in general does not break the universal property of the cross section if particular conditions are required to the spacetime geometry. However, the mass-dependence of the cross section is very sensitive to the spacetime property in the near-horizon regime. Email:[email protected] Email:[email protected] Email:[email protected] 1 It is well-known that the low-energy absorption cross section of the massless particle for the black hole is proportional to the surface area of the horizon [1–6]. This universal property is shown to be maintained for the higher-dimensional objects such as extremal strings and black p-brane [4]. Furthermore, adopting the usual quantum mechanical matching conditions the authors in Ref. [5] have argued that the genuine physical reason for the occurrence of the universal property is the independence of the matching point between the asymptotic and near-horizon solutions. In this letter we will examine whether the universal property of the low-energy absorption cross section is maintained or not in the higher-dimensional extended system when the mass effect of the scalar field is involved. In order to proceed we will adopt the quantum mechanical matching conditions φ∞ω (R) = φ 0 ω(R) (1) d dR φ∞ω (R) = d dR φω(R) which is introduced in Ref. [5]. In Eq.(1) φω and φ 0 ω are the asymptotic and near-horizon solutions respectively of the massive scalar field and thus, Eq.(1) is the matching between them at arbitrary location r = R. We will follow Ref. [5] to check the universality when the scalar field is massive. The mass effect in the scalar field requires an explicit r-dependence of the time-time component of the metric for the derivation of φω. (See Eq.(12)) The mass-dependence of the absorption cross section is very sensitive to the r-dependence of the metric. In spite of it the mass of the scalar particle does not break the universal property of the absorption cross section if particular conditions are required. The spacetime generated by the higher-dimensional object is assumed to be ds = γμνdx dx + f(r)dr + rh(r)dΩn+1 (2) through this letter, where μ, ν = 0, 1, · · ·p. Let us consider the minimally coupled massive scalar in this background, which should satisfy 2 (∆A∆ A −m)Φ = 0. (3) If we assume Φ = eφω(r) which is valid for the low-energy s-wave, and introduce a “tortose” coordinate r∗ as following, dr∗ = dr √