# Magnetoresistance in relativistic hydrodynamics without anomalies

## TL;DR

This paper derives magnetoresistance expressions for strongly interacting relativistic fluids using hydrodynamics, revealing negative magnetoresistance effects without anomalies, applicable to ultraclean metals with emergent Lorentz invariance.

## Contribution

It demonstrates that negative magnetoresistance can occur in non-anomalous relativistic fluids due to gradient expansion effects, expanding understanding beyond anomalous systems.

## Key findings

- Negative magnetoresistance can arise without anomalies in relativistic fluids.
- Resistivity tensor shows angular dependence similar to negative magnetoresistance.
- Magnetic field-dependent corrections and impurities influence magnetoresistance.

## Abstract

We present expressions for the magnetoconductivity and the magnetoresistance of a strongly interacting metal in 3+1 dimensions, derivable from relativistic hydrodynamics. Such an approach is suitable for ultraclean metals with emergent Lorentz invariance. When this relativistic fluid contains chiral anomalies, it is known to exhibit longitudinal negative magnetoresistance. We show that similar effects can arise in non-anomalous relativistic fluids due to the distinctive gradient expansion. In contrast with a Galilean-invariant fluid, the resistivity tensor of a dirty relativistic fluid exhibits similar angular dependence to negative magnetoresistance, even when the constitutive relations and momentum relaxation rate are isotropic. We further account for the effect of magnetic field-dependent corrections to the gradient expansion and the effects of long-wavelength impurities on magnetoresistance. We note that the holographic D3/D7 system exhibits negative magnetoresistance.