Homoclinic accretion solutions in the Schwarzschild-anti-de Sitter spacetime

TL;DR

This paper distinguishes between homoclinic and global accretion solutions in Schwarzschild-anti-de Sitter spacetime, showing the existence of analytic homoclinic solutions for isothermal equations and analyzing their properties.

Contribution

It provides the first analytic homoclinic solutions for isothermal equations in this spacetime and discusses their generic existence and limitations based on matter models.

Findings

Homoclinic solutions exist for certain isothermal equations.

Global solutions exist for relativistic matter models like photon gas.

Upper bound on black hole mass for homoclinic accretion derived.

Abstract

The aim of this paper is to clarify the distinction between homoclinic and standard (global) Bondi-type accretion solutions in the Schwarzschild-anti-de Sitter spacetime. The homoclinic solutions have recently been discovered numerically for polytropic equations of state. Here I show that they exist also for certain isothermal (linear) equations of state, and an analytic solution of this type is obtained. It is argued that the existence of such solutions is generic, although for sufficiently relativistic matter models (photon gas, ultra-hard equation of state) there exist global solutions that can be continued to infinity, similarly to standard Michel's solutions in the Schwarzschild spacetime. In contrast to that global solutions should not exist for matter models with a non-vanishing rest-mass component, and this is demonstrated for polytropes. For homoclinic isothermal solutions I derive an upper bound on the mass of the black hole for which stationary transonic accretion is allowed.