Thermoelectric Transport Coefficients from Charged Solv and Nil Black Holes

TL;DR

This paper investigates charged black hole solutions with Thurston geometries and computes their thermoelectric transport properties, revealing dualities to metallic and insulating phases depending on hyperscaling violation.

Contribution

It introduces new charged black hole solutions with Solv and Nil geometries, including cases with hyperscaling violation, and analyzes their dual field theory transport behaviors.

Findings

Solv and Nil black holes without hyperscaling are dual to metals.

Black holes with hyperscaling violation are dual to insulators.

Transport coefficients vary significantly with geometry and hyperscaling properties.

Abstract

In the present work we study charged black hole solutions of the Einstein-Maxwell 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.