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arXiv · 2210.06161

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

Andrew Mummery
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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 ISCO stress, is constructed by ensuring that it reproduces the leading order asymptotic behaviour of the near-ISCO, Newtonian, and global WKB 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 percent 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.

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Andrew Mummery. 2022-10-11. Asymptotic Green's function solutions of the general relativistic thin disc equations. https://doi.org/10.1093/mnras%2Fstac2846

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