Schwarzschild black hole in the dilatonic domain wall

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($h_{44}=2\varphi$). 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.

10 pages, title changed, a crucial comment on the brane world black hole added, and to appear in Phys. Rev. D

References in corpus (13)

• Modulus Stabilization with Bulk Fields
• Brane-World Black Holes
• Infinitely Large New Dimensions
• Supergravity on the Brane
• Black string instabilities in anti-de Sitter space
• Gauge invariant formalism for second order perturbations of Schwarzschild spacetimes
• Black Diamonds at Brane Junctions
• Second order perturbations of a Schwarzschild black hole: inclusion of odd parity perturbations
• Randall-Sundrum Gauge in the Brane World
• Metric Fluctuations in Brane Worlds
• Solitons in Brane Worlds II
• Comment on "Metric Fluctuations in Brane Worlds"
• S-wave absorption of scalars by noncommutative D3-branes

Cited by in corpus (8)

• Quasinormal Modes and Stability Criterion of Dilatonic Black Hole in 1+1 and 4+1 Dimensions
• Curved dilatonic brane worlds
• Brick Walls on the Brane
• Scalar Perturbations of two-dimensional Horava-Lifshitz Black Holes
• U(1) Gauge Field of the Kaluza-Klein Theory in the Presence of Branes
• Quintessence and Brane world scenarios
• Scalar potential from de Sitter brane in 5D and effective cosmological constant
• Entropy of BTZ black strings in the brick wall approach