Asymptotic Green’s function solutions of the general relativistic thin disc equations

Abstract

ABSTRACT The leading order Green’s function solutions of the general relativistic thin disc equations are computed, using a pseudo-Newtonian potential and asymptotic Laplace mode matching techniques. This solution, valid for a vanishing innermost stable circular orbit (ISCO) stress, is constructed by ensuring that it reproduces the leading order asymptotic behaviour of the near-ISCO, Newtonian, and global Wentzel–Kramers–Brillouin limits. Despite the simplifications used in constructing this solution, it is typically accurate, for all values of the Kerr spin parameter a and at all radii, to less than a per cent of the full numerically calculated solutions of the general relativistic disc equations. These solutions will be of use in studying time-dependent accretion discs surrounding Kerr black holes.