Some properties of domain wall solution in the Randall–Sundrum model

Properties of the domain wall (kink) solution in the five-dimensional Randall–Sundrum model are examined both analytically and numerically. The configuration is derived by the bulk Higgs mechanism. We focus on (1) the convergence property of the solution, (2) the stablity of the solution, (3) the non-singular property of the Riemann curvature and (4) the behaviours of the warp factor and the Higgs field. It is found that the bulk curvature changes the sign around the surface of the wall. We also present some exact solutions for two simple cases: (a) the no-potential case, (b) the cosmological term-dominated case. Both solutions have the (naked) curvature singularity. We can regard the domain wall solution as a singularity resolution of the exact solutions.