Abstract
In the present work we study charged black hole solutions of the EinsteinMaxwell action that have Thurston geometries on its near horizon region. In particular we find solutions with charged Solv and Nil geometry horizons. We also find Nil black holes with hyperscaling violation. For all our solutions we compute the thermoelectric DC transport coefficients of the corresponding dual field theory. We find that the Solv and Nil black holes without hyperscaling violation are dual to metals while those with hyperscaling violation are dual to insulators.
Highlights
In the present work we study charged black hole solutions of the EinsteinMaxwell action that have Thurston geometries on its near horizon region
We find that the Solv and Nil black holes without hyperscaling violation are dual to metals while those with hyperscaling violation are dual to insulators
DμF μν = 0, Rμν and we will look for solutions with charged Solv and Nil horizons that will be dual to field theories at finite temperature T and chemical potential μ without translational invariance
Summary
Charged and dyonic solvgeometry black holes will require to numerically integrate the Einstein-Maxwell equations of motion (1.3). Non relativistic geometries are interesting in its own right in the context of AdS/CFT because they offer a playground to study dual non-conformal field theories [5]. Where rh corresponds to the position of the horizon and μ to the chemical potential of the dual field theory. The equation of motion for the Maxwell fields is automatically satisfied for Ay, consistency of the Einsteins equations requires Ay = rhμ. This means that charged solvgeometry black holes must be dyonic within the simple metric ansatz (2.1).
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