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Bianchi attractors are homogeneous but anisotropic extremal black branehorizons. We study the $AdS_3 \times \mathbb{H}^2$ solution which is a specialcase of Bianchi type III in a $U(1)_R$ gauged supergravity. For a wide range ofvalues for certain free parameters in gauged supergravity, there exist a largeclass of solutions that satisfy conditions for the attractor mechanism to hold.We investigate the response of the solution against linearized fluctuations ofthe scalar field. The sufficient conditions for the attractor mechanism ensurethat there exist a solution for the scalar fluctuation which dies out at thehorizon. Furthermore, we solve for the gauge field and metric fluctuations thatare sourced by scalar fluctuations and show that they are well behaved near thehorizon. Thus, we have an example of a stable Bianchi attractor in gaugedsupergravity. We also analyze the Killing spinor equations of gaugedsupergravity in the background of our solution. We find that a radial Killingspinor consistent with the Bianchi III symmetry breaks supersymmetry.

Stable Bianchi III attractor in $U(1)_R$ gauged supergravity