Schwarzschild black hole in the dilatonic domain wall - art. no. 064034

In the dilatonic domain wall model, we study the Schwarzschild black hole a s a solution to the Kaluza-Klein zero mode effective action which is equiva lent 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 intersecti on of the black cigar with the brane. The black cigar located far from the five-dimensional anti-de Sitter (AdS(5)) horizon is known to be stable, but any explicit calculation for stability of the RS black hole at z = 0 has n ot yet been performed. Here its stability is investigated against the z-ind ependent perturbations composed of odd-even parities of graviton (h(mu nu)) and BD scalar(h(44)=2 phi). It seems that the RS black hole is classically unstable because it has a potential instability at a wavelength lambda >1/ (2k). However, this is not allowed inside an AdS(5) box of the size 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.