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After the nontrivial quantum parameters $Omega_{n}$ and quantum potentials $V_{n}$ obtained in our previous research, the circumstance of a real scalar wave in the bulk is studied with the similar method of Brevik (2001). The equation of a massless scalar field is solved numerically under the boundary conditions near the inner horizon $r_{e}$ and the outer horizon $r_{c}$. Unlike the usual wave function $Psi_{omega l}$ in 4D, quantum number $n$ introduces a new functions $Psi_{omega l n}$, whose potentials are higher and wider with bigger n. Using the tangent approximation, a full boundary value problem about the Schr$ddot{o}$dinger-like equation is solved. With a convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients are obtained. If extra dimension does exist and is visible at the neighborhood of black holes, the unique wave function $Psi_{omega l n}$ may say something to it.
The Nariai black hole, whose two horizons are lying close to each other, is an extreme and important case in the research of black hole. In this paper we study the evolution of a massless scalar field scattered around in 5D Schwarzschild-de Sitter bl
As one exact candidate of the higher dimensional black hole, the 5D Ricci-flat Schwarzschild-de Sitter black string space presents something interesting. In this paper, we give a numerical solution to the real scalar field around the Nariai black hol
As one candidate of the higher dimensional black holes, the 5D Ricci-flat black string is considered in this paper. By means of a non-trivial potential $V_{n}$, the quasi-normal modes of a massless scalar field around this black string space is studi
Assuming that a scalar field controls the inflationary era, we examine the combined effects of string and $f(R)$ gravity corrections on the inflationary dynamics of canonical scalar field inflation, imposing the constraint that the speed of the primo
As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter black-hole. The complex rela