# Exact relativistic viscous fluid solutions in near horizon extremal Kerr background

## TL;DR

This paper constructs exact relativistic viscous fluid solutions with electromagnetic fields in the near-horizon extremal Kerr background, aiding the understanding of accretion physics near black hole horizons, especially for nearly extremal black holes.

## Contribution

It provides the first exact relativistic viscous fluid solutions in the near-horizon extremal Kerr geometry, incorporating electromagnetic fields.

## Key findings

- Solutions applicable to accretion disk modeling near extremal black holes
- Potential connections to Kerr/CFT correspondence
- Enhanced understanding of physics near the ISCO in extremal Kerr black holes

## Abstract

Realistic accretion disk models require a number of ingredients, including viscous fluids, electromagnetic fields and general relativistic corrections. Close to the innermost stable circular orbit (ISCO) the latter can be appreciable and (quasi-)Newtonian approximations become unreliable. This is particularly true for nearly extremal black holes like GRS 1915+105, where the ISCO almost coincides with the black hole horizon. To describe the physics close to the ISCO adequately in a simplified model we approximate the nearly extremal Kerr geometry by the near-horizon extremal Kerr geometry and construct in this background relativistic viscous fluid solutions with electromagnetic fields. We discuss some applications of our solutions and possible relations to the Kerr/CFT correspondence.