Schwarzschild Black Hole in the Dilatonic Domain Wall

In the dilatonic domain wall model, we study the Schwarzschild black hole as a solution to the Kaluza-Klein (KK) zero mode effective action which is equivalent to the Brans-Dicke (BD) model with a potential. This can describe the large Randall-Sundrum (RS) black hole whose horizon is to be the intersection of the black cigar with the brane. The black cigar located far from the AdS 5-horizon is known to be stable, but any explicit calculation for stability of the RS black hole at z = 0 is not yet performed. Here its stability is investigated against the z-independent perturbations composed of odd, even parities of graviton (h µν) and BD scalar(h 44 = 2ϕ). It seems that the RS black hole is classically unstable because it has a potential instability at wavelength with λ > 1/(2k). However, this is not allowed inside an AdS 5-box of the size with 1/(2k). Thus the RS black hole becomes stable. The RS black hole can be considered as a stable remnant at z = 0 of the black cigar.