Project:

The discovery of active galactic nuclei and quasars as
well as compact objects like supermassive black holes, neutron stars
and pulsars prompted the realisation that their high energy emission
was due to the liberation of the gravitational potential energy of infalling material. Bondi accretion models a polytrope fluid accelerating towards a star with a Newtonian gravitational potential. This was later
extended to full general relativity by Michel who examined accretion onto a Schwarzschild black hole.
Modelling accreting systems in full general relativity becomes significantly more challenging when one includes more realistic phenomena like viscosity, magnetic fields, turbulence and radiative processes.
Paczynski and Wiita introduced a gravitational potential that approximates many features of the Schwarzschild black hole in general relativity. The system's dynamical behaviour is governed by the Navier-Stokes equations which are substantially simpler to analyse than those arising from a fully relativistic treatment. Regular black holes admit event horizons but not singularities. They arise in a number of hypothetical modifications to general relativity.
In this project we will follow a recently discovered algorithm and derive a pseudo-Newtonian potential for a number of regular black holes eg. the Bardeen and Hayward metrics. We will then solve the problem of
matter accreting onto regular black holes. Comparisons will be made with the equivalent fully relativistic problems. This project encompasses aspects of fluid mechanics, Newtonian gravity, astrophysics and
general relativity. The techniques employed will be largely analytical with some numerical methods like solving ODEs, root finding and curve sketching.

Requirements for students to address:

General relativity, electromagnetic theory and fluid mechanics