Two Schwarzschild black holes in the dilatonic domain wall

We study two Schwarzschild black holes as the spherically symmetric solution to the zero mode effective action in the dilatonic domain wall model. This corresponds to the dilatonic version of the Randall-Sundrum(RS) model. Further this can be reduced to the Brans-Dicke(BD) model with the potential, which leads to the RS black hole. In the absence of the potential, one finds the known BD black hole. The stability of these black holes is investigated against small perturbations composed of odd, even parities of graviton(h µν) and the BD scalar(h 44). We find that the BD black hole is classically stable , whereas the RS black hole is classically unstable. However, if the BD scalar does not have the perturbation, one can find the stable RS black hole. This confirms that the RS brane world can be extended to the spherically symmetric spacetime only when h 44 = h 4µ = 0.