62 citations · 729 across the 63 of their papers we have counts for
55 papers · 1 filter
Kerr geodesics on conformal projection diagrams
Przemysław Podleśny, Patryk Mach
We provide a rigorous representation of timelike geodesics in the maximally extended Kerr spacetime, using projection diagrams introduced by Chruściel, Ölz, and Szybka. In contrast…
Relativistic figures of equilibrium in the Wald magnetosphere
Paweł Doruchowski, Patryk Mach, Audrey Trova +1
We consider a self-gravitating, rigidly rotating charged perfect fluid immersed in the Wald magnetosphere, constructed out of two linearly independent Killing vectors present in st…
A Monte Carlo approach to stationary kinetic disks in the Kerr spacetime
Ghafran Khan, Patryk Mach
We extend a recently proposed Monte Carlo scheme for computing stationary solutions of the general-relativistic Vlasov equation to the Kerr spacetime. As an example, we focus on ra…
Bondi-type accretion onto a Kerr black hole in the kinetic regime
Patryk Mach, Mehrab Momennia, Olivier Sarbach
We derive an exact solution representing a Bondi-type stationary accretion of a kinetic (Vlasov) gas onto the Kerr black hole. The solution is exact in the sense that relevant phys…
Accretion of a Vlasov gas by a Kerr black hole
Patryk Mach, Mehrab Momennia, Olivier Sarbach
We investigate the accretion of a collisionless, relativistic kinetic gas by a rotating Kerr black hole, assuming that at infinity the state of the gas is described by a distributi…
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…
Finite collisionless accretion disks in the Kerr spacetime
Ghafran Khan, Patryk Mach
We construct general-relativistic kinetic models of stationary finite accretion disks in the Kerr spacetime. Our analysis generalizes a previous model of razor-thin accretion disks…
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…
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…
Accretion of the relativistic Vlasov gas in the equatorial plane of the Kerr black hole
Adam Cieślik, Patryk Mach, Andrzej Odrzywolek
We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. The solution is specified by imposing asymptotic bo…
Revisiting timelike and null geodesics in the Schwarzschild spacetime: general expressions in terms of Weierstrass elliptic functions
Adam Cieślik, Patryk Mach
The theory of Schwarzschild geodesics is revisited. Basing on a result by Weierstrass and Biermann, we derive a formula describing all non radial, timelike and null trajectories in…
Accretion of the relativistic Vlasov gas onto a moving Schwarzschild black hole: Low-temperature limit and numerical aspects
Patryk Mach, Andrzej Odrzywolek
New developments related to our recent study of the accretion of the Vlasov gas onto a moving Schwarzschild black hole are presented. We discuss the low-temperature limit of the ma…
Steady critical accretion onto black holes: selfgravity and sonic point characteristics
Patryk Mach, Edward Malec
The spherically symmetric steady accretion of polytropic perfect fluids onto a black hole is the simplest flow model that can demonstrate effects of backreaction (selfgravity). It…
Toroidal magnetic fields in self-gravitating disks around black holes
Wojciech Dyba, Patryk Mach, Mikolaj Pietrzynski
We investigate stationary models of magnetized, self-gravitating disks around black holes. The disks are assumed to rotate according to a recently introduced Keplerian rotation law…
Stationary massive disks around black holes: realistic equation of state and bifurcation
Wojciech Kulczycki, Patryk Mach, Edward Malec
We study stationary and axially symmetric black hole-disk systems, assuming a combination of the DD2 and Timmes-Swesty equations of state and a three-parameter family of rotation l…
Accretion of Dark Matter onto a Moving Schwarzschild Black Hole: An Exact Solution
Patryk Mach, Andrzej Odrzywolek
We investigate accretion of dark matter onto a moving Schwarzschild black hole. The dark matter is modeled by the collisionless Vlasov gas, assumed to be in thermal equilibrium at…
Accretion of the relativistic Vlasov gas onto a moving Schwarzschild black hole: Exact solutions
Patryk Mach, Andrzej Odrzywolek
We derive an exact, axially symmetric solution representing stationary accretion of the relativistic, collisionless Vlasov gas onto a moving Schwarzschild black hole. The gas is as…
Accretion of the Vlasov gas on Reissner-Nordström black holes
Adam Cieślik, Patryk Mach
We investigate stationary spherically symmetric accretion of the relativistic Vlasov gas on Reissner-Nordström black holes. The model is based on a recent analysis done by Rioseco…
A toy model of hyperboloidal approach to quasinormal modes
Piotr Bizoń, Tadeusz Chmaj, Patryk Mach
We consider a scalar field propagating in the static region of the two dimensional de Sitter space. This simple system is used to illustrate the advantages of hyperboloidal foliati…