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 disfavoured 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 favourable at D > 12 + p , whereas the non-uniform smeared branes are favourable at D > 14 + p near the extremality.