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 (24)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• The Hierarchy Problem and New Dimensions at a Millimeter
• New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
• Kaluza-Klein Gravity
• Black Holes in Theories with Large Extra Dimensions: a Review
• TeV Scale Superstring and Extra Dimensions
• Calculable Corrections to Brane Black Hole Decay I: The Scalar Case
• Hawking Radiation from a (4+n)-dimensional Black Hole: Exact Results for the Schwarzschild Phase
• Calculable Corrections to Brane Black Hole Decay II: Greybody Factors for Spin 1/2 and 1
• Black Hole Radiation in the Brane World and Recoil Effect
• Radiative falloff in Schwarzschild-de Sitter spacetime
• Equivalence Between Space-Time-Matter and Brane-World Theories
• Bulk and Brane Decay of a (4+n)-Dimensional Schwarzschild-De-Sitter Black Hole: Scalar Radiation
• Solar System Tests of Higher-Dimensional Gravity
• Scalar radiation emitted from a source rotating around a black hole
• Classical confinement of test particles in higher-dimensional models: stability criteria and a new energy condition
• Gauge-Dependent Cosmological "Constant"
• Spacetime Measurements in Kaluza-Klein Gravity
• Interaction of Hawking radiation with static sources outside a Schwarzschild black hole
• Exact Global Solutions of Brane Universes and Big Bounce
• The Real Scalar Field in Schwarzschild-de Sitter Spacetime
• 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

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• 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
• Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes
• The Numerical Solution of Scalar Field for Nariai Case in 5D Ricci-flat SdS Black String Space with Polynomial Approximation