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Abstract In this paper, we consider rotating multistate boson stars with quartic self-interactions. In contrast to the nodeless quartic-boson stars in [1], the self-interacting multistate boson stars (SIMBSs) have two types of nodes, including the 1 S 2 S and 1 S 2 P states. We show the mass M of SIMBSs as a function of the synchronized frequency ω, and the nonsynchronized frequency ω 2 for three different cases. Moreover, for the case of two coexisting states with self-interacting potential, we study the mass M of SIMBSs versus the angular momentum J for the synchronized frequency ω and the nonsynchronized frequency ω 2. Furthermore, for three different cases, we analyze the coexisting phase with both the ground and first excited states for SIMBSs. We also calculate the maximum value of coupling parameter Λ, and find the coupling parameter Λ exists the finite range.

Abstract Motivated by the novel asymptotically global AdS4 solutions with deforming horizon in [21], we analyze the boundary metric with even multipolar differential rotation and numerically construct a family of deforming solutions with quadrupolar differential rotation boundary, including two classes of solutions: solitons and black holes. In contrast o solutions with dipolar differential rotation boundary, we find that even though the norm of Killing vector ∂ t becomes spacelike for certain regions of polar angle θ when ε > 2, solitons and black holes with quadrupolar differential rotation still exist and do not develop hair due to superradiance. Moreover, at the same temperature, the horizonal deformation of quadrupolar rotation is smaller than that of dipolar rotation. Furthermore, we also study the entropy and quasinormal modes of the solutions, which have the analogous properties to that of dipolar rotation.