Abstract
Bianchi attractors are homogeneous but anisotropic extremal black brane horizons. We study the $AdS_3 \times \mathbb{H}^2$ solution which is a special case of Bianchi type III in a $U(1)_R$ gauged supergravity. For a wide range of values for certain free parameters in gauged supergravity, there exist a large class of solutions that satisfy conditions for the attractor mechanism to hold. We investigate the response of the solution against linearized fluctuations of the scalar field. The sufficient conditions for the attractor mechanism ensure that there exist a solution for the scalar fluctuation which dies out at the horizon. Furthermore, we solve for the gauge field and metric fluctuations that are sourced by scalar fluctuations and show that they are well behaved near the horizon. Thus, we have an example of a stable Bianchi attractor in gauged supergravity. We also analyze the Killing spinor equations of gauged supergravity in the background of our solution. We find that a radial Killing spinor consistent with the Bianchi III symmetry breaks supersymmetry.
Highlights
New classes of extremal solutions exhibiting reduced symmetries have been found [24, 25]
We solve for the gauge field and metric fluctuations that are sourced by scalar fluctuations and show that they are well behaved near the horizon
We studied the AdS3 × H2 solution which is a special case of the Bianchi type III class in U(1)R gauged supergravity
Summary
We begin with a quick review of some elements of the Bianchi III symmetry. The Bianchi classification of real Lie algebras in three dimensions is well known in the literature [30, 31]. We are interested in five dimensional black brane horizons with homogeneous symmetries in the spatial directions These geometries are obtained from gravity coupled to simple matter in the presence of a cosmological constant and are known as the Bianchi attractors [24, 25]. For the purposes of this article, we construct a simple type III solution in Einstein-Maxwell theory sourced by a single massless gauge field and a cosmological constant. We have a magnetic type III solution sourced by a massless gauge field and parametrized by βt, which satisfies the condition βt. We have a magnetic type III solution sourced by a massless gauge field and parametrized by βt, which satisfies the condition βt2 We construct a similar solution in U(1)R gauged supergravity
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