# Anisotropic Dyonic Black Brane and its Effects on Hydrodynamics

## TL;DR

This paper develops an $SL(2,R)$ invariant framework for anisotropic charged black holes in massive gravity, deriving conductivity expressions and analyzing their behavior under external magnetic fields using holographic methods.

## Contribution

It introduces an $SL(2,R)$ invariant approach to anisotropic black branes and derives general conductivity formulas applicable in holographic models.

## Key findings

- Conductivities can be computed from horizon data in magnetic fields.
- Numerical results demonstrate the impact of anisotropy and magnetic fields on holographic conductivities.
- The framework provides a new way to analyze anisotropic strongly coupled systems.

## Abstract

We construct $SL(2,R)$ invariant in anisotropic medium, with a dual anisotropic charged black hole geometry in massive gravity. We show how to obtain $SL(2,R)$ elements in terms of new degrees of freedom for Electromagnetic configuration, and construct the general expressions for conductivity with $SL(2,R)$ invariant. The holographic conductivities can be calculated using horizon data in an external magnetic field, and we show the numerical results using the linear response theory.