The Real Solution to Scalar Field Equation in 5D Black String Space

Abstract

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 ${\Psi }_{\omega ln}$, 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 ${\Psi }_{\omega ln}$ may say something to it.

10 pages, 6 figures. To appear in Gen. Rel. Grav

References in corpus (2)

• Using (4+1) split and energy conditions to study the induced matter in 5D Ricc-flat cosmology
• Radiation and Potential Barriers of a 5D Black String Solution

Cited by in corpus (6)

• Quasi-Normal Modes of Massless Scalar Field around the 5D Ricci-flat Black String
• Quantum Statistical Entropy and Minimal Length of 5D Ricci-flat Black String with Generalized Uncertainty Principle
• The Real Scalar Field Equation for Nariai Black Hole in the 5D Schwarzschild-de Sitter Black String Space
• The Dynamic Behavior of Quantum Statistical Entropy in 5D Ricci-flat Black String with Thin-layer Approach
• Real Scalar Field Scattering with Polynomial Approximation around Schwarzschild-de Sitter Black-hole
• The Numerical Solution of Scalar Field for Nariai Case in 5D Ricci-flat SdS Black String Space with Polynomial Approximation