29 citations · 33 across the 7 of their papers we have counts for
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Semiclassical causal geodesics: Minkowski spacetime case
Adam Cieślik, Andrzej Góźdź, Patryk Mach +2
We use an integral quantization model based on the Heisenberg-Weyl group to describe the motion of a spinless particle in the Minkowski background spacetime. This work is a sequel…
Kerr Geodesics in horizon-penetrating Kerr coordinates: description in terms of Weierstrass functions
Zuzanna Bakun, Angelika Łukanty, Anastasiia Untilova +2
We revisit the theory of timelike and null geodesics in the (extended) Kerr spacetime. This work is a sequel to a recent paper by Cieślik, Hackmann, and Mach, who applied the so-ca…
Integral quantization based on the Heisenberg-Weyl group
Aleksandra Pȩdrak, Andrzej Góźdź, Włodzimierz Piechocki +2
We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based o…
Monte Carlo methods for stationary solutions of general-relativistic Vlasov systems: Planar accretion onto a moving Schwarzschild black hole
Adam Cieślik, Patryk Mach, Andrzej Odrzywolek
We perform Monte Carlo simulations of stationary planar accretion of a collisionless gas onto a moving Schwarzschild black hole. In this work -- a sequel to our previous paper on t…
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…
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…