62 citations · 729 across the 63 of their papers we have counts for
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Monte Carlo methods for stationary solutions of general-relativistic Vlasov systems: Collisionless accretion onto black holes
Patryk Mach, Adam Cieślik, Andrzej Odrzywolek
We develop a Monte Carlo simulation method for computing stationary solutions of the general-relativistic Vlasov equation describing a gas of non-colliding particles. As specific e…
Equatorial accretion on the Kerr black hole
Patryk Mach, Andrzej Odrzywołek
We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. At infinity the gas obeys the Maxwell-Jüttner distr…
Kerr Geodesics in Terms of Weierstrass Elliptic Functions
Adam Cieślik, Eva Hackmann, Patryk Mach
We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parameterized explicitly by constants of motion -- the energy,…
Timelike and null geodesics in the Schwarzschild space-time: Analytical solutions
Adam Cieślik, Patryk Mach
The theory of Schwarzschild geodesics is revisited. Using a theorem due to Weierstrass and Biermann, we derive concise formulas describing all timelike and null trajectories in ter…