Schwarzschild black hole in the dilatonic domain wall

TL;DR

This paper investigates the stability of Schwarzschild black holes in the dilatonic domain wall model, finding that they are stable within the Randall-Sundrum framework due to size constraints, and describes their relation to black cigars.

Contribution

It provides a stability analysis of RS black holes in the dilatonic domain wall model, showing they are stable when considering the AdS$_5$-box size constraints.

Findings

RS black hole is classically unstable at certain wavelengths

Stability is restored within the AdS$_5$-box size

RS black hole is a stable remnant of the black cigar

Abstract

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 ($h_{\mu\nu}$) and BD scalar($h_{44} = 2\phi $). It seems that the RS black hole is classically unstable because it has a potential instability at wavelength with $\lambda > 1/(2k)$. 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.