Almost-BPS solutions in multi-center Taub-NUT

Microstates of colinear black holes embedded in a multi-center Taub-NUT spacetime are sought in 4 dimensions. A set of coupled ordinary partial differential equations are obtained and solved for almost-BPS states, where some supersymmetry is preserved in the context of N=2 supergravity in 4 dimensions. The regularity of solutions is being carefully considered and we ensure that no CTC (closed time-like curves) are present. The larger framework is that of 11-dimensional N=2 supergravity and the current theory is obtained by compactifying down to 4 dimensions.