The Numerical Solution Of Scalar Field Radiation In 5D Black String Space

The 5D Ricci-flat Schwarzschild-de Sitter (SdS) black hole, which contains an induced cosmological constant, is derived from the exact solution of empty 5D Einstein equation of the Space-Time-Matter (STM) theory. This solution can be embed into a brane world scenario and constitutes a 5D Ricci-flat SdS black string space (a 5D black string space, for short).In this paper we embed the 5D Ricci-flat SdS solution into RS 2-brane model. That is, we suppose that there are two SM branes with opposite tension in the 5D bulk. The two branes have reflecting symmetry with regard to the extra dimension and are placed at two fix end-points of the extra dimension respectively. Our world is supposed on one of the 3-branes. According to Hawking radiation theory, the black hole of 5D black string space radiates various particles into bulk. In this paper we take the massless scalar particles as test particles to study its movement in the 5D black string space background and the influence of the fifth dimension to the radiation.During the course of solving Klein-Gordon equation, we find that the existence of extra dimension affects the radial motion of the scalar particles. Especially under given conditions, the particles will feel a quantized potential barrier. It is known from qualitative analysis that the smaller magnitude of extra dimension has more impact on the potential. As a result, the reflection of the particles is more intense, that is, Hawking radiation will be more forceful. So studying the radial movement in the potential field is significant to the conception of using black hole radiation to detect the extra dimension. The radial equation turns to a Schrodinger-like master equation after tortoise coordinate alternation. Before solving the master equation, we adopt the Nariai case to determine the parameter and ascertain the boundary conditions. Then under the polynomial approximation, the numerical solution of the radial equation is obtained through mathmatica software. The ultimate result shows that the wave is similar to harmonic one between the horizons and piles up rapidly near the horizons. Furthermore, the approximate synchronous accumulation near the two horizons shows that their traits are homologous.