# Accretion within the innermost stable circular orbit: analytical thermodynamic solutions in the adiabatic limit

## TL;DR

This paper derives the first analytical thermodynamic solutions for thin accretion flows within the ISCO of a Kerr black hole, revealing unique temperature behaviors independent of black hole spin and flow assumptions.

## Contribution

It introduces a new class of non-circular, non-radial analytical solutions for accretion flows inside the ISCO, valid in the adiabatic, radiative-loss neglecting regime.

## Key findings

- Solutions cool within a specific radius range before heating up closer to the black hole.
- Radiative temperature peaks can occur inside the ISCO, not in the main disc.
- Solutions are independent of black hole spin and equation of state assumptions.

## Abstract

We present analytical solutions for the thermodynamic (temperature, pressure, density, etc.) properties of thin accretion flows in the region within the innermost stable circular orbit (ISCO) of a Kerr black hole, the first analytical solutions of their kind. These solutions are constructed in the adiabatic limit and neglect radiative losses, an idealisation valid for a restricted region of parameter space. We highlight a number of remarkable properties of these solutions, including that these solutions cool for radii $r_I/2 < r < r_I$, before increasing in temperature for $0 < r < r_I/2$, independent of black hole spin and assumptions regarding the equation of state of the accretion flow. The radiative temperature of these solutions can, for some values of the free parameters of the theory, peak within the ISCO and not in the main body of the disc. These solutions represent a fundamentally new class of analytical accretion solutions, which are both non-circular and non-radial in character.