Accretion with back reaction

TL;DR

This paper analytically investigates how back reaction effects influence stationary spherical accretion near black hole horizons, revealing divergence issues for extremal black holes and implications for black hole thermodynamics.

Contribution

It provides the first analytical calculation of back reaction effects on accretion flows near black hole horizons, highlighting limitations of the test fluid approximation for extreme black holes.

Findings

Back reaction corrections depend only on fluid accretion rate.

Corrections diverge for extremely charged black holes.

Test fluid approximation fails for extreme black holes.

Abstract

We calculate analytically a back reaction of the stationary spherical accretion flow near the event horizon and near the inner Cauchy horizon of the charged black hole. It is shown that corresponding back-reaction corrections to the black hole metric depend only on the fluid accretion rate and diverge in the case of an extremely charged black hole. In result, the test fluid approximation for stationary accretion is violated for extreme black holes. This behavior of the accreting black hole is in accordance with the third law of black hole thermodynamics, forbidding the practical attainability of the extreme state.