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The leading order Green's function solutions of the general relativistic thindisc equations are computed, using a pseudo-Newtonian potential and asymptoticLaplace mode matching techniques. This solution, valid for a vanishing ISCOstress, is constructed by ensuring that it reproduces the leading orderasymptotic behaviour of the near-ISCO, Newtonian, and global WKB limits.Despite the simplifications used in constructing this solution, it is typicallyaccurate, for all values of the Kerr spin parameter $a$ and at all radii, toless than a percent of the full numerically calculated solutions of the generalrelativistic disc equations. These solutions will be of use in studyingtime-dependent accretion discs surrounding Kerr black holes.

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