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

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.

arXiv comment9 pages, 7 figures, 4 appendices. Accepted for publication in MNRAS

References in corpus (5)

• The swallowing of a quark star by a black hole
• Propagating mass accretion rate fluctuations in X-ray binaries under the influence of viscous diffusion
• The general relativistic thin disc evolution equation
• The evolution of Kerr discs and late-time tidal disruption event light curves
• Evolution of relativistic thin discs with a finite ISCO stress: II. Late time behaviour

Cited by in corpus (3)

• Fundamental scaling relationships revealed in the optical light curves of tidal disruption events
• Extending the theory of propagating fluctuations: the first fully relativistic treatment and analytical Fourier-Green's functions
• The X-ray variability of tidal disruption events