# Chiral vortical effect with finite rotation, temperature, and curvature

## TL;DR

This paper calculates the axial current in curved space with rotation and temperature, revealing relations between curvature, mass, and chiral effects, with potential astrophysical implications.

## Contribution

It introduces a novel relation between curvature-induced mass shifts and the chiral vortical effect, linking gravitational anomalies to axial currents in rotating systems.

## Key findings

- Finite curvature and mass modify the chiral vortical effect.
- A product of angular velocity and curvature shares anomaly coefficients.
- Potential application to jet formation in rotating astrophysical objects.

## Abstract

We perform an explicit calculation of the axial current at finite rotation and temperature in curved space. We find that finite curvature and mass corrections to the chiral vortical effect satisfy a relation of the chiral gap effect, that is, a fermion mass-shift by a scalar curvature. We also point out that a product term of the angular velocity and the scalar curvature shares the same coefficient as the mixed gravitational chiral anomaly. We discuss possible applications of the curvature induced chiral vortical effect to rotating astrophysical compact objects described by the Kerr metric. Instead of direct calculation we assume that the Chern-Simons current can approximate the physical axial current. We make a proposal that the chiral vortical current from rotating compact objects could provide a novel microscopic mechanism behind the generation of collimated jets.