Multi-black hole configurations on the cylinder

Understand

We construct the metric of new multi-black hole configurations on a d-dimensional cylinder R^{d-1} x S^1, in the limit of small total mass (or equivalently in the limit of a large cylinder).

• These solutions are valid to first order in the total mass and describe configurations with several small black holes located at different points along the circle direction of the cylinder.
• We explain that a static configuration of black holes is required to be in equilibrium such that the external force on each black hole is zero, and we examine the resulting conditions.
• The first-order corrected thermodynamics of the solutions is obtained and a Newtonian interpretation of it is given.