Abstract
We find neutral and charged black brane solutions with axion fields in the context of a conformally coupled gravitational theory in four dimensions. These solutions describe anti--de Sitter (AdS) black branes supported by axion fields that break translational invariance at the boundary, which provides momentum dissipation. The conformally coupled scalar field is regular inside and outside the event horizon and there is no need for any self-interaction, obtaining in this way solutions without fine-tuned parameters. We analyze the thermodynamics of our solutions considering the effects of the axionic charges. In asymptotically AdS configurations, the axionic and electric charges are related, implying vanishing scalar field contributions to the mass. The rotating solution is obtained by means of a Lorentz boost having angular momentum sustained by the axion parameter. We compute the holographic DC conductivity and we show how it is affected by the inclusion of the conformal scalar field, which provides a temperature-independent behavior. Finally, we include a $k$-essence term that modifies the DC conductivity and provides more general behaviors.
Highlights
We find neutral and charged black brane solutions with axion fields in the context of a conformally coupled gravitational theory in four dimensions
These solutions describe anti–de Sitter (AdS) black branes supported by axion fields that break translational invariance at the boundary, which provides momentum dissipation
We compute the holographic DC conductivity and we show how it is affected by the inclusion of the conformal scalar field, which provides a temperature-independent behavior
Summary
For any well-posed gravitational theory such as Einstein’s general relativity (GR) or any of its extensions, the existence of black hole solutions is a matter of primary interest. The AdS=CFT correspondence [28] establishes a duality between gravitational theories in D dimensions and conformal field theories in the (D − 1)dimensional boundary In this scenario, black holes became suitable laboratories to study strongly coupled systems, opening a new range of applicability of gravitational solutions at the service of condensed matter systems [29,30]. This paper is devoted to the construction of AdS black brane solutions with a conformally coupled scalar field where the translational invariance at the boundary is broken by means of axion fields that depend linearly on the base manifold directions. This solution represents the generalization to the conformal.
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