Entropy of the Randall–Sundrum black brane world in the brick-wall method

We calculate the entropy of the brane-world black hole in the Randall–Sundrum (RS) model by using the brick-wall method. The modes along the extra dimension are semi-classically quantized on the extra dimension. The number of modes in the extra dimension is given as a simple form with the help of the RS mass relation, and then the entropy for the scalar modes in the five-dimensional spacetime is described by the two-dimensional area of the black brane world.