Patryk Mach's homepage

Publications

Aleksandra Pedrak, Andrzej Gozdz, Wlodzimierz Piechocki, Patryk Mach, Adam Cieslik, Integral quantization based on the Heisenberg-Weyl group (2024) arXiv
Zuzanna Bakun, Angelika Lukanty, Anastasiia Untilova, Adam Cieslik, Patryk Mach, Kerr Geodesics in horizon-penetrating Kerr coordinates: description in terms of Weierstrass functions (2024) arXiv
Adam Cieslik, Patryk Mach, Andrzej Odrzywolek, Monte Carlo methods for stationary solutions of general-relativistic Vlasov systems: Planar accretion onto a moving Schwarzschild black hole, Phys. Rev. D 110, 084014 (2024) https://doi.org/10.1103/PhysRevD.110.084014, arXiv
Patryk Mach, Adam Cieslik, Andrzej Odrzywolek, Monte Carlo methods for stationary solutions of general-relativistic Vlasov systems: Collisionless accretion onto black holes, Phys. Rev. D 108, 124057 (2023) https://doi.org/10.1103/PhysRevD.108.124057, arXiv
Patryk Mach, Andrzej Odrzywolek, Equatorial accretion on the Kerr black hole, Acta Phys. Pol. B Proc. Suppl. 16, 6-A13 (2023) https://doi.org/10.5506/APhysPolBSupp.16.6-A13, arXiv
Adam Cieslik, Patryk Mach, Eva Hackmann, Kerr Geodesics in Terms of Weierstrass Elliptic Functions, Phys. Rev. D 108, 024056 (2023) https://doi.org/10.1103/PhysRevD.108.024056, arXiv
Adam Cieslik, Patryk Mach, Timelike and null geodesics in the Schwarzschild space-time: Analytical solutions, Acta Phys. Pol. B Proc. Suppl. 16, 6-A10 (2023) https://doi.org/10.5506/APhysPolBSupp.16.6-A10, arXiv
Adam Cieslik, Patryk Mach, Andrzej Odrzywolek, Accretion of the relativistic Vlasov gas in the equatorial plane of the Kerr black hole, Phys. Rev. D 106, 104056 (2022) https://doi.org/10.1103/PhysRevD.106.104056, arXiv
Adam Cieslik, Patryk Mach, Revisiting timelike and null geodesics in the Schwarzschild spacetime: general expressions in terms of Weierstrass elliptic functions, Class. Quantum Grav. 39, 225003 (2022) https://doi.org/10.1088/1361-6382/ac95f2, arXiv
Patryk Mach, Edward Malec, Steady critical accretion onto black holes: Self-gravity and sonic point characteristics, Phys. Rev. D 105, 104012 (2022) https://doi.org/10.1103/PhysRevD.105.104012, arXiv
Patryk Mach, Andrzej Odrzywolek, Accretion of the Relativistic Vlasov Gas onto a Moving Schwarzschild Black Hole: Low-temperature Limit and Numerical Aspects, Acta Phys. Pol. B Proc. Suppl. 15, 1-A7 (2022) https://doi.org/10.5506/APhysPolBSupp.15.1-A7, arXiv
Wojciech Dyba, Patryk Mach, Mikolaj Pietrzynski, Toroidal magnetic fields in self-gravitating disks around black holes, Phys. Rev. D 104, 044058 (2021) https://doi.org/10.1103/PhysRevD.104.044058, arXiv
Wojciech Kulczycki, Patryk Mach, Edward Malec, Stationary massive disks around black holes: Realistic equation of state and bifurcation, Phys. Rev. D 104, 024005 (2021) https://doi.org/10.1103/PhysRevD.104.024005, arXiv
Patryk Mach, Andrzej Odrzywolek, Accretion of Dark Matter onto a Moving Schwarzschild Black Hole: An Exact Solution, Phys. Rev. Lett. 126, 101104 (2021) https://doi.org/10.1103/PhysRevLett.126.101104, arXiv
Patryk Mach, Andrzej Odrzywolek, Accretion of the relativistic Vlasov gas onto a moving Schwarzschild black hole: Exact solutions, Phys. Rev. D 103, 024044 (2021) https://doi.org/10.1103/PhysRevD.103.024044, arXiv
Adam Cieslik, Patryk Mach, Accretion of the Vlasov gas on Reissner-Nordstrom black holes, Phys. Rev. D 102, 024032 (2020), https://doi.org/10.1103/PhysRevD.102.024032, arXiv
Piotr Bizon, Tadeusz Chmaj, Patryk Mach, A toy model of hyperboloidal approach to quasinormal modes, Acta Phys. Pol. B 51, 1007 (2020) https://doi.org/10.5506/APhysPolB.51.1007, arXiv
Wojciech Dyba, Wojciech Kulczycki, Patryk Mach, Self-gravitating perfect-fluid tori around black holes: Bifurcations, ergoregions, and geometrical properties, Phys. Rev. D 101, 044036 (2020) https://doi.org/10.1103/PhysRevD.101.044036, arXiv
Patryk Mach, Sergio Gimeno-Soler, Jose A. Font, Andrzej Odrzywolek, Michal Pirog, Self-gravitating magnetized tori around black holes in general relativity, Phys. Rev. D 99, 104063 (2019) https://doi.org/10.1103/PhysRevD.99.104063, arXiv
Wojciech Dyba, Patryk Mach, Edward Malec, Modelling general-relativistic disk in OJ 287, Mon. Not. R. Astron. Soc. 486, 3118-3123 (2019) https://doi.org/10.1093/mnras/stz1058, arXiv
Patryk Mach, Yaohua Wang, Naqing Xie, Construction of vacuum initial data by the conformally covariant split system, Class. Quantum Grav. 36, 145001 (2019) https://doi.org/10.1088/1361-6382/ab2781, arXiv
Wojciech Kulczycki, Patryk Mach, Edward Malec, Two mass conjectures on axially symmetric black hole-disk systems, Phys. Rev. D 99, 024004 (2019) https://doi.org/10.1103/PhysRevD.99.024004, arXiv
Janusz Karkowski, Wojciech Kulczycki, Patryk Mach, Edward Malec, Andrzej Odrzywolek, Michal Pirog, Self-gravitating axially symmetric disks in general-relativistic rotation, Phys. Rev. D 97, 104017 (2018) https://doi.org/10.1103/PhysRevD.97.104017, arXiv
Patryk Mach, Jerzy Knopik, Rotating Bowen-York initial data with a positive cosmological constant, Class. Quantum Grav. 35, 145002 (2018) https://doi.org/10.1088/1361-6382/aac585, arXiv
Janusz Karkowski, Wojciech Kulczycki, Patryk Mach, Edward Malec, Andrzej Odrzywolek, Michal Pirog, General-relativistic rotation: self-gravitating fluid tori in Keplerian motion around black holes, Phys. Rev. D 97, 104034 (2018) https://doi.org/10.1103/PhysRevD.97.104034, arXiv
Patryk Mach, Michal Pirog, Jose A. Font, Relativistic Low Angular Momentum Accretion: Long Time Evolution of Hydrodynamical Inviscid Flows, Class. Quantum Grav. 35, 095005 (2018) https://doi.org/10.1088/1361-6382/aab333, arXiv
Filip Ficek, Patryk Mach, Planar domain walls in black hole spacetime, Phys. Rev. D 97, 044012 (2018) https://doi.org/10.1103/PhysRevD.97.044012, arXiv
Patryk Mach, Naqing Xie, Toroidal marginally outer trapped surfaces in closed Friedmann-Lemaitre-Robertson-Walker spacetimes: Stability and isoperimetric inequalities, Phys. Rev. D 96, 084050 (2017) https://doi.org/10.1103/PhysRevD.96.084050, arXiv
Janusz Karkowski, Patryk Mach, Edward Malec, Niall O Murchadha, Naqing Xie, Toroidal trapped surfaces and isoperimetric inequalities, Phys. Rev. D 95, 064037 (2017) https://doi.org/10.1103/PhysRevD.95.064037, arXiv
Jerzy Knopik, Patryk Mach, Andrzej Odrzywolek, The shape of a rapidly rotating polytrope with index unity, Mon. Not. R. Astron. Soc. 467, 4965 (2017) https://doi.org/10.1093/mnras/stx164, arXiv
Janusz Karkowski, Patryk Mach, Edward Malec, Michal Pirog, Naqing Xie, Rotating systems, universal features in dragging and antidragging effects, and bounds of angular momentum, Phys. Rev. D 94, 124041 (2016) https://doi.org/10.1103/PhysRevD.94.124041, arXiv
Piotr Bizoń, Patryk Mach, Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space, Trans. Amer. Math. Soc. 369, 2029-2048 (2017) https://doi.org/10.1090/tran/6807, arXiv
Eliana Chaverra, Patryk Mach and Olivier Sarbach, Michel accretion of a polytropic fluid with adiabatic index $\gamma \gt 5/3$: global flows versus homoclinic orbits, Class. Quantum Grav. 33, 105016 (2016) https://doi.org/10.1088/0264-9381/33/10/105016, arXiv
Patryk Mach, Edward Malec, Michal Pirog, General-relativistic rotation laws in rotating fluid bodies, new weak-field effects and the post-Newtonian expansion, The Fourteenth Marcel Grossmann Meeting: pp. 1994-1999 (2017) https://doi.org/10.1142/9789813226609_0215, arXiv
Jerzy Knopik, Patryk Mach, Edward Malec, General-relativistic rotation laws in rotating fluid bodies: constant linear velocity, Acta Phys. Pol. B 46, 2451 (2015), https://doi.org/10.5506/APhysPolB.46.2451, arXiv
Piotr Jaranowski, Patryk Mach, Edward Malec, Michal Pirog, Virial tests for post-Newtonian stationary black-hole—disk systems, Journal of Physics: Conference Series 600, 012011 (2015) https://doi.org/10.1088/1742-6596/600/1/012011, arXiv
Patryk Mach, Homoclinic accretion solutions in the Schwarzschil-(anti)-de Sitter space-time, Phys. Rev. D 91, 084016 (2015) https://doi.org/10.1103/PhysRevD.91.084016, arXiv
Patryk Mach, Edward Malec, General-relativistic rotation laws in rotating fluid bodies, Phys. Rev. D 91, 124053 (2015) https://doi.org/10.1103/PhysRevD.91.124053, arXiv
Piotr Jaranowski, Patryk Mach, Edward Malec, Michal Pirog, General-relativistic versus Newtonian: Geometric dragging and dynamic antidragging in stationary self-gravitating disks in the first post-Newtonian approximation, Phys. Rev. D 91, 024039 (2015) https://doi.org/10.1103/PhysRevD.91.024039, arXiv
Patryk Mach, Niall O Murchadha, Spherically symmetric Riemannian manifolds of constant scalar curvature and their conformally flat representations, Class. Quantum Grav. 31, 135001 (2014) https://doi.org/10.1088/0264-9381/31/13/135001, arXiv
Patryk Mach, Edward Malec, Stability of relativistic Bondi accretion in Schwarzschild-(anti-)de Sitter spacetimes, Phys. Rev. D 88, 084055 (2013) https://doi.org/10.1103/PhysRevD.88.084055, arXiv
Patryk Mach, Edward Malec, Janusz Karkowski, Spherical steady accretion flows: Dependence on the cosmological constant, exact isothermal solutions, and applications to cosmology, Phys. Rev. D 88, 084056 (2013) https://doi.org/10.1103/PhysRevD.88.084056, arXiv
Patryk Mach, Edward Malec, Walter Simon, Self-gravitating Newtonian disks revisited, in: García-Parrado A., Mena F., Moura F., Vaz E. (eds) Progress in Mathematical Relativity, Gravitation and Cosmology, Springer Proceedings in Mathematics & Statistics, vol 60, Springer, Berlin, Heidelberg, pp. 305-309 (2014) https://doi.org/10.1007/978-3-642-40157-2_43, arXiv
Patryk Mach, Edward Malec, Michal Pirog, Geometry of Keplerian disk systems and bounds on masses of their components, Acta Phys. Pol. B 44, 107 (2013) https://doi.org/10.5506/APhysPolB.44.107, arXiv
Patryk Mach, Edward Malec, Michal Pirog, Estimating masses of Keplerian disk systems: the case of AGN in NGC 4258, Acta Phys. Pol. B 43, 2141 (2012) https://doi.org/10.5506/APhysPolB.43.2141, arXiv
Patryk Mach, Instabilities of the Riemann problem in relativistic hydrodynamics, AIP Conf. Proc. 1458, 459 (2012) https://doi.org/10.1063/1.4734459
Patryk Mach, All solutions of the n = 5 Lane-Emden equation, J. Math. Phys. 53, 062503 (2012) https://doi.org/10.1063/1.4725414, arXiv
Patryk Mach, Virial theorem for radiating accretion discs, Mon. Not. R. Astron. Soc. 422, 772 (2012) https://doi.org/10.1111/j.1365-2966.2012.20658.x, arXiv
Patryk Mach, Walter Simon, (In)finite extent of stationary perfect fluids in Newtonian theory, Annales Henri Poincare 14, 159 (2013) https://doi.org/10.1007/s00023-012-0181-0, arXiv
Patryk Mach, Edward Malec, Accretion and Structure of Radiating Disks, Astron. Astrophys. 541, A128 (2012) https://doi.org/10.1051/0004-6361/201015755, arXiv
Patryk Mach, Corrugation instabilities of the Riemann problem in relativistic hydrodynamics, (2011) arXiv
Patryk Mach, Edward Malec, Self-gravitating discs and the Sobolev inequality, Mon. Not. R. Astron. Soc. 411, 1313 (2011) https://doi.org/10.1111/j.1365-2966.2010.17764.x, arXiv
Patryk Mach, Malgorzata Pietka, Exact solution of the hydrodynamical Riemann problem with nonzero tangential velocities and the ultrarelativistic equation of state, Phys. Rev. E 81, 046313 (2010) https://doi.org/10.1103/PhysRevE.81.046313, arXiv
Patryk Mach, Analytic Solutions of the Riemann Problem in Relativistic Hydrodynamics and their Numerical Applications, Acta Phys. Pol B Proceedings Supplement 2, 575 (2009) Acta Phys. Pol. B archive, arXiv
Patryk Mach, On the stability of steady general-relativistic accretion and analogue black holes, Reports on Mathematical Physics 64, 257 (2009) https://doi.org/10.1016/S0034-4877(09)90031-3, arXiv.
Patryk Mach, Edward Malec, Stability of self-gravitating accreting flows, Phys. Rev. D 78, 124016 (2008) https://doi.org/10.1103/PhysRevD.78.124016, arXiv
Patryk Mach, Selfgravitation and stability in spherical accretion, Acta. Phys. Pol. B 38, 3935 (2007) Acta Phys. Pol. B archive
Bogusz Kinasiewicz, Patryk Mach, From polytropic to barotropic perfect fluids in general-relativistic hydrodynamics, Acta Phys. Pol. B 38, 39 (2007). Acta Phys. Pol. B archive, arXiv
Janusz Karkowski, Bogusz Kinasiewicz, Patryk Mach, Edward Malec, Zdobyslaw Swierczynski, General relativistic accretion with backreaction, Proceedings of the MG11 Meeting on General Relativity 23-29 July 2006, World Scientific (2008) https://doi.org/10.1142/9789812834300_0404, arXiv
Bogusz Kinasiewicz, Patryk Mach, Edward Malec, Selfgravitation in general-relativistic accretion of steady fluids, International Journal of Geometric Methods in Modern Physics 4, 197 (2007) https://doi.org/10.1142/S0219887807001953, arXiv
Janusz Karkowski, Bogusz Kinasiewicz, Patryk Mach, Edward Malec, Zdobyslaw Swierczynski, Universality and backreaction in a general-relativistic accretion of steady fluids, Phys. Rev. D 73, 021503(R) (2006) https://doi.org/10.1103/PhysRevD.73.021503, arXiv
Patryk Mach, On the propagation of non stationary pressure waves in stellar interiors, Acta Phys. Pol. B35, 2479 (2004) Acta. Phys. Pol. B archive, arXiv

Patryk Mach

Current research interests

Publications

Teaching