# Self-similar accretion in thin disks around near-extremal black holes

## TL;DR

This paper introduces a new self-similar radiation-dominated solution for thin accretion disks around near-extremal black holes, highlighting the role of conformal symmetry and providing insights into disk behavior at high spins.

## Contribution

It presents a novel self-similar solution for thin disks near extremal black holes, connecting disk properties with black hole spin and accretion parameters.

## Key findings

- Self-similar solution valid in high-spin regime
- Viscosity parameter expressed in terms of spin and accretion rate
- Approach of exact solution to self-similar form near ISCO

## Abstract

Near-maximally spinning black holes display conformal symmetry in their near-horizon region, which is therefore the locus of critical phenomena. In this paper, we revisit the Novikov-Thorne accretion thin disk model and find a new self-similar radiation-dominated solution in the extremely high spin regime. Motivated by the self-consistency of the model, we require that matter flows at the sound speed at the innermost stable circular orbit (ISCO). We observe that, when the disk pressure is dominated by radiation at the ISCO, which occurs for the best-fitting Novikov-Thorne model of GRS 1915+105, the Shakura-Sunyaev viscosity parameter can be expressed in terms of the spin, mass accretion rate and radiative efficiency. We quantitatively describe how the exact thin disk solution approaches the self-similar solution in the vicinity of the ISCO and for increasing spins.