On non-uniform smeared black branes

We investigate charged dilatonic black p-branes smeared on a transverse circle. The system can be reduced to neutral vacuum black branes, and we perform static perturbations for the reduced system to construct non-uniform solutions. At each order a single master equation is derived, and the Gregory-Laflamme critical wavelength is determined. Based on the non-uniform solutions, we discuss thermodynamic properties of this system and argue that in a microcanonical ensemble the non-uniform smeared branes are entropically disfavored even near the extremality, if the spacetime dimension is D ≤ 13+p, which is the critical dimension for the vacuum case. However, the critical dimension is not universal. In a canonical ensemble the vacuum non-uniform black branes are thermodynamically favorable at D > 12 + p, whereas the non-uniform smeared branes are favorable at D > 14 + p near the extremality. Electronic address: kudoh at utap.phys.s.u-tokyo.ac.jp Electronic address: umpei at gravity.phys.waseda.ac.jp