Critical lumpy black holes in AdSp×Sq

In this paper we study lumpy black holes with AdS${}_p \times S^q$ asymptotics, where the isometry group coming from sphere factor is broken down to SO($q$). Depending on values of $p$ and $q$, these are solutions a certain Supergravity theory particular gauge field. We have considered $(p,q) = (5,5)$ (4,7)$, corresponding type IIB supergravity in ten dimensions eleven-dimensional respectively. These theories presumably contain an infinite spectrum families holes, labeled by harmonic number $\ell$, whose endpoints solution space merge another different horizon topology. numerically constructed first four solutions, $\ell 1, 2^+, 2^-$ $3$. show that geometry near merger well-described cone over triple product spheres, thus extending Kol's local model present asymptotics. Interestingly, presence non-trivial fluxes internal implies no longer Ricci flat. This conical manifold accounts for behavior physical quantities sufficiently close critical point. Additionally, vacuum expectation dual scalar operators approach their power law exponents dictated bulk.